Masaru Kamata - Academia.edu (original) (raw)

Papers by Masaru Kamata

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2013

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2006

arXiv: High Energy Physics - Theory, 2016

We derive a discretized version of the nonlinear O(3) sigma model through a discrete theory of co... more We derive a discretized version of the nonlinear O(3) sigma model through a discrete theory of complex analysis of Mercat. Adopting a simple two-dimensional rectangular lattice, we obtain a discrete energy E^{disc.} and a discrete area \cal{A}(f)^{disc.}, where a function f is related to a stereographic projection governed by a unit vector {\boldmath n} of the model. Both discrete energy and area satisfy the inequality E^{disc.} \ge |\cal{A}(f)^{disc.}|, which is saturated if and only if the function f is discrete (anti-)holomorphic. The vector {\boldmath n} parametrizing the function describes classical discrete (anti-)instanton solutions on the lattice. Two discrete instanton solutions are illustrated, which are derived from polynomials up to degree two in z. Except for a factor 2, the discrete energy and the area tend to the usual continuous energy E and the area \cal{A}(f)=4 \pi q, q \in \pi_2(S^2), respectively, as the lattice spacings tend to zero.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2005

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2006

Physics Letters B, 1995

The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensi... more The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Bañados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation Er = ±Bˆ, which is imposed on the orthonormal basis components of the electric field Er and the magnetic field Bˆ. This solution describes an electrically charged extreme black hole with mass M = 8πGQ 2 e , angular momentum J = ±8πGQ 2 e /|Λ| 1/2 and electric charge Q e. Although the coordinate components of the electric field E r and the magnetic field B have singularities on the horizon at r = (4πGQ 2 e /|Λ|) 1/2 , the spacetime has the same value of constant negative curvature R = 6Λ as that of Bañados et al.

Physics Letters B, 1997

We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equati... more We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equations with a negative cosmological constant in 2+1 spacetime dimensions assuming a (anti-)self dual condition between the electromagnetic fields. In a coordinate condition there appears a logarithmic divergence in the angular momentum at spatial infinity. We show how it is to be regularized by taking the contribution from the boundary into account. We show another coordinate condition which leads to a finite angular momentum though it brings about a peculiar spacetime topology.

Mathematics and Computers in Simulation, 2009

There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)sel... more There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)self-dual (ASD) Yang-Mills equations. This conjecture is supported by many concrete examples, e.g., the Nahm equations. In this work, we consider a situation that if the ASD conditions are slightly loosened, as to how it affects the integrability of the equations. For this purpose, we consider a q-analog of the Nahm equations, as a non-ASD system. The analysis is performed on the reduced system which is a q-analog of the Euler-Arnold top, by the singularity confinement test and the estimation of the algebraic entropy.

Journal of Physics A: Mathematical and General, 2002

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional ord... more An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/N-th order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding out the new extensions of the KP hierarchy, brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional order pseudo-differential operators.

Physics Letters B, 1999

The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theori... more The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theories, is applied to an infinite dimensional l 2 vector space, and as a consequence, a family of (anti-)selfdual configurations with a parameter q is obtained for SU(2) Yang-Mills theory. This l 2 formulation can be seen as a q-analog of Nahm's monopole construction, so that the configuration approaches the BPS monopole at q → 1 limit.

We present a q-analogue of Nahm's formalism for the BPS monopole, which gives self-dual gaug... more We present a q-analogue of Nahm's formalism for the BPS monopole, which gives self-dual gauge fields with a deformation parameter q. The theory of the basic hypergeometric series is used in our formalism. In the limit q -> 1 the gauge fields approach the BPS monopole and Nahm's result is reproduced.

2+1 dimensional charged black hole with (anti-)self dual Maxwell fields

The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensi... more The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Bañados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation Eˆr = ±Bˆ, which is imposed on the orthonormal basis components of the electric field Eˆr and the magnetic field Bˆ. This solution describes an electrically charged extreme black hole with mass M = 8πGQ2 e, angular momentum J = ±8πGQ2 e /|Λ|1/2 and electric charge Qe. Although the coordinate components of the electric field Er and the magnetic field B have singularities on the horizon at r = (4πGQ2 e /|Λ|)1/2, the spacetime has the same value of constant negative curvature R = 6Λ as that of Bañados et al. MIRAMARE –TRIESTE

arXiv: High Energy Physics - Theory, 2013

To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry,... more To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry, [J_3, \phi]=0 and [J_3, A_{\pm}]=\pm A_{\pm}, is imposed on the Higgs scalar \phi and the gauge fields A_{\pm} of the system, respectively, where J_3 is a sum of the third components of the orbital angular momenta and the generators of the SU(2). The circular symmetry and the equation \bar{D}\phi=0 yield onstant, generally nonzero, vacuum expectation values for {\rm Tr}(\phi^{2}). The equation 4F_{z\bar{z}}=[\phi, \phi^{*}] yields a system of differential equations which govern the circularly symmetric field configurations and an exact solution to these equations in a pure gauge form with nontrivial Higgs scalar is obtained.

In the preceding paper (1999 Phys.Lett. B463 257), the authors presented a q-analog of the ADHMN ... more In the preceding paper (1999 Phys.Lett. B463 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.

arXiv: High Energy Physics - Theory, 2016

We examine a discrete version of the two-dimensional nonlinear O(3)O(3)O(3) sigma model derived from di... more We examine a discrete version of the two-dimensional nonlinear O(3)O(3)O(3) sigma model derived from discrete complex analysis. We adopt two lattices, one rectangular, the other polar. We define a discrete energy E(f)rmdisc.E({f})^{\rm disc.}E(f)rmdisc. and a discrete area calA(f)rmdisc.{\cal{A}}({f})^{\rm disc.}calA(f)rmdisc., where the function fff is related to a stereographic projection governed by a unit vector of the model. The discrete energy and area satisfy the inequality E(f)rmdisc.ge∣calA(f)rmdisc.∣E({f})^{\rm disc.} \ge |{\cal{A}}({f})^{\rm disc.}|E(f)rmdisc.ge∣calA(f)rmdisc.∣, which is saturated if and only if the function fff is discrete (anti-)holomorphic. We show for the rectangular lattice that, except for a factor 2, the discrete energy and the area tend to the usual continuous energy E(f)E({f})E(f) and the area calA(f)=4piN,,,Ninpi_2(S2){\cal{A}}({f})=4 \pi N, \,\,N\in \pi_2(S^2)calA(f)=4piN,,,Ninpi_2(S2) as the lattice spacings tend to zero. In the polar lattice, we section the plane by 2M2M2M lines passing through the origin into 2M2M2M equal sectors and place vertices radially in a geometric progression with a common ratio $q...

Il Nuovo Cimento B, 1981

Summary The spherically symmetric Julia-Zee dyon solution of the coupled Yang-Mills-Higgs system... more Summary The spherically symmetric Julia-Zee dyon solution of the coupled Yang-Mills-Higgs systems is studied in curved space-time. An exact solution for which the space-time metric takes the Reissner-Nordström form is presented.

To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry,... more To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry, [J_3, \phi]=0 and [J_3, A_{\pm}]=\pm A_{\pm}, is imposed on the Higgs scalar \phi and the gauge fields A_{\pm} of the system, respectively, where J_3 is a sum of the third components of the orbital angular momenta and the generators of the SU(2). The circular symmetry and the equation \bar{D}\phi=0 yield onstant, generally nonzero, vacuum expectation values for {\rm Tr}(\phi^{2}). The equation 4F_{z\bar{z}}=[\phi, \phi^{*}] yields a system of differential equations which govern the circularly symmetric field configurations and an exact solution to these equations in a pure gauge form with nontrivial Higgs scalar is obtained.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2013

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2006

arXiv: High Energy Physics - Theory, 2016

We derive a discretized version of the nonlinear O(3) sigma model through a discrete theory of co... more We derive a discretized version of the nonlinear O(3) sigma model through a discrete theory of complex analysis of Mercat. Adopting a simple two-dimensional rectangular lattice, we obtain a discrete energy E^{disc.} and a discrete area \cal{A}(f)^{disc.}, where a function f is related to a stereographic projection governed by a unit vector {\boldmath n} of the model. Both discrete energy and area satisfy the inequality E^{disc.} \ge |\cal{A}(f)^{disc.}|, which is saturated if and only if the function f is discrete (anti-)holomorphic. The vector {\boldmath n} parametrizing the function describes classical discrete (anti-)instanton solutions on the lattice. Two discrete instanton solutions are illustrated, which are derived from polynomials up to degree two in z. Except for a factor 2, the discrete energy and the area tend to the usual continuous energy E and the area \cal{A}(f)=4 \pi q, q \in \pi_2(S^2), respectively, as the lattice spacings tend to zero.

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2005

Meeting Abstracts of the Physical Society of Japan (Nihon Butsuri Gakkai koen gaiyoshu), 2006

Physics Letters B, 1995

The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensi... more The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Bañados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation Er = ±Bˆ, which is imposed on the orthonormal basis components of the electric field Er and the magnetic field Bˆ. This solution describes an electrically charged extreme black hole with mass M = 8πGQ 2 e , angular momentum J = ±8πGQ 2 e /|Λ| 1/2 and electric charge Q e. Although the coordinate components of the electric field E r and the magnetic field B have singularities on the horizon at r = (4πGQ 2 e /|Λ|) 1/2 , the spacetime has the same value of constant negative curvature R = 6Λ as that of Bañados et al.

Physics Letters B, 1997

We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equati... more We discuss the exact electrically charged BTZ black hole solutions to the Einstein-Maxwell equations with a negative cosmological constant in 2+1 spacetime dimensions assuming a (anti-)self dual condition between the electromagnetic fields. In a coordinate condition there appears a logarithmic divergence in the angular momentum at spatial infinity. We show how it is to be regularized by taking the contribution from the boundary into account. We show another coordinate condition which leads to a finite angular momentum though it brings about a peculiar spacetime topology.

Mathematics and Computers in Simulation, 2009

There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)sel... more There is a conjecture by Ward that almost all of integrable equations are derived from (anti-)self-dual (ASD) Yang-Mills equations. This conjecture is supported by many concrete examples, e.g., the Nahm equations. In this work, we consider a situation that if the ASD conditions are slightly loosened, as to how it affects the integrability of the equations. For this purpose, we consider a q-analog of the Nahm equations, as a non-ASD system. The analysis is performed on the reduced system which is a q-analog of the Euler-Arnold top, by the singularity confinement test and the estimation of the algebraic entropy.

Journal of Physics A: Mathematical and General, 2002

An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional ord... more An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/N-th order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding out the new extensions of the KP hierarchy, brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional order pseudo-differential operators.

Physics Letters B, 1999

The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theori... more The ADHM construction, which yields (anti-)selfdual configurations in classical Yang-Mills theories, is applied to an infinite dimensional l 2 vector space, and as a consequence, a family of (anti-)selfdual configurations with a parameter q is obtained for SU(2) Yang-Mills theory. This l 2 formulation can be seen as a q-analog of Nahm's monopole construction, so that the configuration approaches the BPS monopole at q → 1 limit.

We present a q-analogue of Nahm's formalism for the BPS monopole, which gives self-dual gaug... more We present a q-analogue of Nahm's formalism for the BPS monopole, which gives self-dual gauge fields with a deformation parameter q. The theory of the basic hypergeometric series is used in our formalism. In the limit q -> 1 the gauge fields approach the BPS monopole and Nahm's result is reproduced.

2+1 dimensional charged black hole with (anti-)self dual Maxwell fields

The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensi... more The Einstein-Maxwell equations with a negative cosmological constant Λ in 2 + 1 spacetime dimensions discussed by Bañados, Teitelboim and Zanelli are solved by assuming a self (anti-self) dual equation Eˆr = ±Bˆ, which is imposed on the orthonormal basis components of the electric field Eˆr and the magnetic field Bˆ. This solution describes an electrically charged extreme black hole with mass M = 8πGQ2 e, angular momentum J = ±8πGQ2 e /|Λ|1/2 and electric charge Qe. Although the coordinate components of the electric field Er and the magnetic field B have singularities on the horizon at r = (4πGQ2 e /|Λ|)1/2, the spacetime has the same value of constant negative curvature R = 6Λ as that of Bañados et al. MIRAMARE –TRIESTE

arXiv: High Energy Physics - Theory, 2013

To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry,... more To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry, [J_3, \phi]=0 and [J_3, A_{\pm}]=\pm A_{\pm}, is imposed on the Higgs scalar \phi and the gauge fields A_{\pm} of the system, respectively, where J_3 is a sum of the third components of the orbital angular momenta and the generators of the SU(2). The circular symmetry and the equation \bar{D}\phi=0 yield onstant, generally nonzero, vacuum expectation values for {\rm Tr}(\phi^{2}). The equation 4F_{z\bar{z}}=[\phi, \phi^{*}] yields a system of differential equations which govern the circularly symmetric field configurations and an exact solution to these equations in a pure gauge form with nontrivial Higgs scalar is obtained.

In the preceding paper (1999 Phys.Lett. B463 257), the authors presented a q-analog of the ADHMN ... more In the preceding paper (1999 Phys.Lett. B463 257), the authors presented a q-analog of the ADHMN construction and obtained a family of anti-selfdual configurations with a parameter q for classical SU(2) Yang-Mills theory in four-dimensional Euclidean space. The family of solutions can be seen as a q-analog of the single BPS monopole preserving (anti-)selfduality. Further discussion is made on the relation to axisymmetric ansatz on anti-selfdual equation given by Witten in the late seventies. It is found that the q-exponential functions familiar in q-analysis appear as analytic functions categorizing the anti-selfdual configurations yielded by axisymmetric ansatz.

arXiv: High Energy Physics - Theory, 2016

We examine a discrete version of the two-dimensional nonlinear O(3)O(3)O(3) sigma model derived from di... more We examine a discrete version of the two-dimensional nonlinear O(3)O(3)O(3) sigma model derived from discrete complex analysis. We adopt two lattices, one rectangular, the other polar. We define a discrete energy E(f)rmdisc.E({f})^{\rm disc.}E(f)rmdisc. and a discrete area calA(f)rmdisc.{\cal{A}}({f})^{\rm disc.}calA(f)rmdisc., where the function fff is related to a stereographic projection governed by a unit vector of the model. The discrete energy and area satisfy the inequality E(f)rmdisc.ge∣calA(f)rmdisc.∣E({f})^{\rm disc.} \ge |{\cal{A}}({f})^{\rm disc.}|E(f)rmdisc.ge∣calA(f)rmdisc.∣, which is saturated if and only if the function fff is discrete (anti-)holomorphic. We show for the rectangular lattice that, except for a factor 2, the discrete energy and the area tend to the usual continuous energy E(f)E({f})E(f) and the area calA(f)=4piN,,,Ninpi_2(S2){\cal{A}}({f})=4 \pi N, \,\,N\in \pi_2(S^2)calA(f)=4piN,,,Ninpi_2(S2) as the lattice spacings tend to zero. In the polar lattice, we section the plane by 2M2M2M lines passing through the origin into 2M2M2M equal sectors and place vertices radially in a geometric progression with a common ratio $q...

Il Nuovo Cimento B, 1981

Summary The spherically symmetric Julia-Zee dyon solution of the coupled Yang-Mills-Higgs system... more Summary The spherically symmetric Julia-Zee dyon solution of the coupled Yang-Mills-Higgs systems is studied in curved space-time. An exact solution for which the space-time metric takes the Reissner-Nordström form is presented.

To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry,... more To study circularly symmetric field configurations in the SU(2) Hitchin system an SO(2) symmetry, [J_3, \phi]=0 and [J_3, A_{\pm}]=\pm A_{\pm}, is imposed on the Higgs scalar \phi and the gauge fields A_{\pm} of the system, respectively, where J_3 is a sum of the third components of the orbital angular momenta and the generators of the SU(2). The circular symmetry and the equation \bar{D}\phi=0 yield onstant, generally nonzero, vacuum expectation values for {\rm Tr}(\phi^{2}). The equation 4F_{z\bar{z}}=[\phi, \phi^{*}] yields a system of differential equations which govern the circularly symmetric field configurations and an exact solution to these equations in a pure gauge form with nontrivial Higgs scalar is obtained.