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Papers by R. Alvarez-Estrada

Nuclear Physics B, 1971

... NorthHoIiand Publishing Company ON THE CONSTRUCTION OF PION PHOTOPRODUCTION AMPLITUDES FROM E... more ... NorthHoIiand Publishing Company ON THE CONSTRUCTION OF PION PHOTOPRODUCTION AMPLITUDES FROM EXPERIMENTAL DATA RF ALVAREZ ESTRADA * Laboratoire de ... incoming photons and ini tially unpolarized protons is for = R) Pji(R) 1 + 5 [joji(+, 1)]2 DI Jay ...

A freely rotating linear chain, formed by N (N~2) atoms with N-1 "bonds" of fixed lengths, is stu... more A freely rotating linear chain, formed by N (N~2) atoms with N-1 "bonds" of fixed lengths, is studied in three spatial dimensions. The classical (c) theory of that constrained system is formulated in terms of the classical transverse momentuma, , and angular momentum lJ, associated to the jth "bond" (j =1,. .. , N-1). The classical Poisson brackets of the Cartesian components ofa, , and 1, , are shown to close an algebra. The quantization of the chain in spherical polar coordinates is carried out. The resulting "curved-space" quantization yields modified angular momenta I,. Quantum-mechanical transverse momenta (e,) are constructed. The commutators of the Cartesian components of e, and 1j satisfy a closed Lie algebra, formally similar to the classical one for Poisson brackets. Using e~'s and 1,-'s, the quantum theory is shown to be consistent by itself and, via the correspondence principle, with the classical one. Several properties of e, and the modified 1, are given: some sets of eigenfunctions (modified spherical harmonics, etc.) and uncertainty relations. As an example, the case of N =3 atoms in two spatial dimensions is worked out. The peculiar properties of the chain regarding distinguishability at the quantum level play an important role in justifying the absence of a "Boltzmann counting" factor [(N-1)! ] in its classical statistical distribution. The physical limitations and the methodological virtues of the model at the classical and quantum levels, and its relationship to previous works by different authors, are discussed.

We analyze the finite temperature (T) extension of the Wess-Zumino-Witten functional, discussed i... more We analyze the finite temperature (T) extension of the Wess-Zumino-Witten functional, discussed in a previous work, to one loop in chiral perturbation theory. As a phenomenological application, we calculate finite temperature corrections to the amplitude of π 0 decay into two photons. This calculation is performed in three limits: i) T/Mπ << 1, ii) the chiral limit at finite T and iii) T/Mπ>> 1 (Mπ being the pion mass). The T-corrections tend to vanish in the chiral limit, where only the kaon contribution remains (although it is exponentially suppressed). FT/UCM/15-93 1 The extension of the Wess-Zumino-Witten (WZW) anomalous lagrangian [1] for the finite temperature (T = 0) case has been analyzed recently [2]. Instead of the usual S 4 compactification of Euclidean space-time at T = 0 [1], a S 1 ×S 3 one was employed for T = 0. Our task is now to evaluate one-loop effects using the S 1 ×S 3 lagrangian, in the trivial (pionic) sector with baryon number NB = 0. In particula...

A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitativ... more A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitatively those produced in a heavy-ion collision, is described by a scalar φ 4 quantum field in (1+3)-dimensional Minkowski space. For high temperature and large temporal and spatial scales, we justify that classical statistical mechanics including quantum renormalization effects describe approximately the gas: nonequilibrium dimensional reduction (NEDR). As a source of hints, we treat the gas at equilibrium in real-time formalism and obtain simplifications for high temperature and large spatial scales, thereby extending a useful equilibrium dimensional reduction known for the imaginary-time formalism. By assumption, the nonequilibrium initial state of the gas, not far from thermal equilibrium, includes interactions and inhomogeneities. We use nonequilibrium real-time generating functionals and correlators at nonzero temperature. In the NEDR regime, our arguments yield: 1) renormalized correlators simplify, 2) the perturbative series for those simplified correlators can be resummed into a new nonequilibrium generating functional, Z r,dr , which is super-renormalizable and includes renormalization effects (large position-dependent thermal self-energies and effective couplings). Z r,dr could enable to study nonperturbatively changes in the phase structures of the field, by proceeding from the nonequilibrium quantum regime to the NEDR one.

In this paper, an account of a fit to the usual electromagnetic form factors (G~, G~, G~, G~) of ... more In this paper, an account of a fit to the usual electromagnetic form factors (G~, G~, G~, G~) of proton and neutron is presented. A theoretical study of form factors (f. f.) has been made from the standpoint of causality, using the linear-system theory (~), which will be published elsewhere; it leads to the conclusion that f. f. are analytic functions of w (the total center-of-mass energy for annihilation reactions like e-e + ~ 7-~ P]5) in the half-plane Im w > 0. In Im w < 0, the isoscalar and isovector f.f. G s, G v (j = M, E; GS.V= (G~• G~)/2) may contain products o] pairs o] poles, symmetric with respect to Rew-0; each pair represents a resonance with the same quantum numbers as the f. f. itself, if it is not far from Imw ~ 0. This suggests that f.f. may be fitted by multiplicative ]ormulae, at least approximately. We will test this hypothesis in electron-nucleon scattering, where w2-~-q2~O (w = ~-i~r q2 being the squared momentum transfer in (GeV/c) ~. The foregoing, the consideration of the experimental decrease of f.f. at large q2 and the fact that the o) and ~ mesons have the appropriate quantum numbers lead to the following expression, dominated by these resonances:

A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum ... more A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum variables (e's), associated to internal rotations and generic ofthese models, are exhibited. The e's and the angular momentum operators generate a rank-two semisimple Lie algebra. The associated Lie group is non-compact. The self-adjointness ofthe Hamiltonian is established. SI Notice that i-!~in eq. (23) of ref. [1] should be replaced by all "bond" distances, masses and (large) frequencies HC-(2M)'fl~M,C

The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated.... more The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated. The imaginary-time formalism of quantum field theory at finite temperature and pathintegral methods are used. For the Schwinger model, the partition function displays two features: (i) no physical (transverse) photons exist in 1+1 dimensions; (ii) the theory also describes just free massive bosons. For the Thirring model, the partition function equals that for free massless fermions. The complete thermodynamical propagators and the energies per unit volume at finite temperature are also given.

The P4 theory in 1+d dimensions is analyzed at high temperatures in the imaginary-time formalism.... more The P4 theory in 1+d dimensions is analyzed at high temperatures in the imaginary-time formalism. General results are given for the leading high-temperature contributions to all renormalized Careen's functions. The latter are generated by a high-temperature partition function which describes another P theory in d spatial dimensions with special mass renormalizations. The triviality/ nontriviality of the (P)1+3 theory is discussed briefiy.

The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed a t high ... more The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed a t high temperature to all orders of perturbation theory. The imaginary-time formalism is used. The photon self-energy and propagator a t finite tempexature with vanishing frequency are given to second order of perturbation theory. Based upon them, an improved perturbation theory which incorporates Debye screening if formulated. In the infinite-temperature limit, the photon sector becomes equivalent to a massive scalar boson field plus a maaslees pure gauge field and both are decoupled: all connected Green's functions with given external momenta much smaller than the temperature and containing, at least, one closedfermion loop with four or more vertices vanish. An approximate generating functional yielding all leading high-temperature corrections to all connected Green's functions is preaented. The Iadt result leads to establish for one spatial dimension a conjecture of Gross, Pisarski and Yaffe regarding the reduction of &ED to a sort of 144 theory a t high temperature. The leading high temperature contribution to the thermodynamic potential to all perturbativc orders: i) is given in terms of the dominant high temperature contribution to the twopoint photon Green's function for zero frequency, ii) is shown to be both ultraviolet and infrared finite.

Nuclear Physics B, 1971

... NorthHoIiand Publishing Company ON THE CONSTRUCTION OF PION PHOTOPRODUCTION AMPLITUDES FROM E... more ... NorthHoIiand Publishing Company ON THE CONSTRUCTION OF PION PHOTOPRODUCTION AMPLITUDES FROM EXPERIMENTAL DATA RF ALVAREZ ESTRADA * Laboratoire de ... incoming photons and ini tially unpolarized protons is for = R) Pji(R) 1 + 5 [joji(+, 1)]2 DI Jay ...

A freely rotating linear chain, formed by N (N~2) atoms with N-1 "bonds" of fixed lengths, is stu... more A freely rotating linear chain, formed by N (N~2) atoms with N-1 "bonds" of fixed lengths, is studied in three spatial dimensions. The classical (c) theory of that constrained system is formulated in terms of the classical transverse momentuma, , and angular momentum lJ, associated to the jth "bond" (j =1,. .. , N-1). The classical Poisson brackets of the Cartesian components ofa, , and 1, , are shown to close an algebra. The quantization of the chain in spherical polar coordinates is carried out. The resulting "curved-space" quantization yields modified angular momenta I,. Quantum-mechanical transverse momenta (e,) are constructed. The commutators of the Cartesian components of e, and 1j satisfy a closed Lie algebra, formally similar to the classical one for Poisson brackets. Using e~'s and 1,-'s, the quantum theory is shown to be consistent by itself and, via the correspondence principle, with the classical one. Several properties of e, and the modified 1, are given: some sets of eigenfunctions (modified spherical harmonics, etc.) and uncertainty relations. As an example, the case of N =3 atoms in two spatial dimensions is worked out. The peculiar properties of the chain regarding distinguishability at the quantum level play an important role in justifying the absence of a "Boltzmann counting" factor [(N-1)! ] in its classical statistical distribution. The physical limitations and the methodological virtues of the model at the classical and quantum levels, and its relationship to previous works by different authors, are discussed.

We analyze the finite temperature (T) extension of the Wess-Zumino-Witten functional, discussed i... more We analyze the finite temperature (T) extension of the Wess-Zumino-Witten functional, discussed in a previous work, to one loop in chiral perturbation theory. As a phenomenological application, we calculate finite temperature corrections to the amplitude of π 0 decay into two photons. This calculation is performed in three limits: i) T/Mπ << 1, ii) the chiral limit at finite T and iii) T/Mπ>> 1 (Mπ being the pion mass). The T-corrections tend to vanish in the chiral limit, where only the kaon contribution remains (although it is exponentially suppressed). FT/UCM/15-93 1 The extension of the Wess-Zumino-Witten (WZW) anomalous lagrangian [1] for the finite temperature (T = 0) case has been analyzed recently [2]. Instead of the usual S 4 compactification of Euclidean space-time at T = 0 [1], a S 1 ×S 3 one was employed for T = 0. Our task is now to evaluate one-loop effects using the S 1 ×S 3 lagrangian, in the trivial (pionic) sector with baryon number NB = 0. In particula...

A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitativ... more A nonequilibrium quantum gas of interacting relativistic effective mesons, ressembling qualitatively those produced in a heavy-ion collision, is described by a scalar φ 4 quantum field in (1+3)-dimensional Minkowski space. For high temperature and large temporal and spatial scales, we justify that classical statistical mechanics including quantum renormalization effects describe approximately the gas: nonequilibrium dimensional reduction (NEDR). As a source of hints, we treat the gas at equilibrium in real-time formalism and obtain simplifications for high temperature and large spatial scales, thereby extending a useful equilibrium dimensional reduction known for the imaginary-time formalism. By assumption, the nonequilibrium initial state of the gas, not far from thermal equilibrium, includes interactions and inhomogeneities. We use nonequilibrium real-time generating functionals and correlators at nonzero temperature. In the NEDR regime, our arguments yield: 1) renormalized correlators simplify, 2) the perturbative series for those simplified correlators can be resummed into a new nonequilibrium generating functional, Z r,dr , which is super-renormalizable and includes renormalization effects (large position-dependent thermal self-energies and effective couplings). Z r,dr could enable to study nonperturbatively changes in the phase structures of the field, by proceeding from the nonequilibrium quantum regime to the NEDR one.

In this paper, an account of a fit to the usual electromagnetic form factors (G~, G~, G~, G~) of ... more In this paper, an account of a fit to the usual electromagnetic form factors (G~, G~, G~, G~) of proton and neutron is presented. A theoretical study of form factors (f. f.) has been made from the standpoint of causality, using the linear-system theory (~), which will be published elsewhere; it leads to the conclusion that f. f. are analytic functions of w (the total center-of-mass energy for annihilation reactions like e-e + ~ 7-~ P]5) in the half-plane Im w > 0. In Im w < 0, the isoscalar and isovector f.f. G s, G v (j = M, E; GS.V= (G~• G~)/2) may contain products o] pairs o] poles, symmetric with respect to Rew-0; each pair represents a resonance with the same quantum numbers as the f. f. itself, if it is not far from Imw ~ 0. This suggests that f.f. may be fitted by multiplicative ]ormulae, at least approximately. We will test this hypothesis in electron-nucleon scattering, where w2-~-q2~O (w = ~-i~r q2 being the squared momentum transfer in (GeV/c) ~. The foregoing, the consideration of the experimental decrease of f.f. at large q2 and the fact that the o) and ~ mesons have the appropriate quantum numbers lead to the following expression, dominated by these resonances:

A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum ... more A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum variables (e's), associated to internal rotations and generic ofthese models, are exhibited. The e's and the angular momentum operators generate a rank-two semisimple Lie algebra. The associated Lie group is non-compact. The self-adjointness ofthe Hamiltonian is established. SI Notice that i-!~in eq. (23) of ref. [1] should be replaced by all "bond" distances, masses and (large) frequencies HC-(2M)'fl~M,C

The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated.... more The thermodynamical partition functions for both the Schwinger and Thirring models are evaluated. The imaginary-time formalism of quantum field theory at finite temperature and pathintegral methods are used. For the Schwinger model, the partition function displays two features: (i) no physical (transverse) photons exist in 1+1 dimensions; (ii) the theory also describes just free massive bosons. For the Thirring model, the partition function equals that for free massless fermions. The complete thermodynamical propagators and the energies per unit volume at finite temperature are also given.

The P4 theory in 1+d dimensions is analyzed at high temperatures in the imaginary-time formalism.... more The P4 theory in 1+d dimensions is analyzed at high temperatures in the imaginary-time formalism. General results are given for the leading high-temperature contributions to all renormalized Careen's functions. The latter are generated by a high-temperature partition function which describes another P theory in d spatial dimensions with special mass renormalizations. The triviality/ nontriviality of the (P)1+3 theory is discussed briefiy.

The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed a t high ... more The photon sector of Quantum Electrodynamics (QED) in one spatial dimension is analyzed a t high temperature to all orders of perturbation theory. The imaginary-time formalism is used. The photon self-energy and propagator a t finite tempexature with vanishing frequency are given to second order of perturbation theory. Based upon them, an improved perturbation theory which incorporates Debye screening if formulated. In the infinite-temperature limit, the photon sector becomes equivalent to a massive scalar boson field plus a maaslees pure gauge field and both are decoupled: all connected Green's functions with given external momenta much smaller than the temperature and containing, at least, one closedfermion loop with four or more vertices vanish. An approximate generating functional yielding all leading high-temperature corrections to all connected Green's functions is preaented. The Iadt result leads to establish for one spatial dimension a conjecture of Gross, Pisarski and Yaffe regarding the reduction of &ED to a sort of 144 theory a t high temperature. The leading high temperature contribution to the thermodynamic potential to all perturbativc orders: i) is given in terms of the dominant high temperature contribution to the twopoint photon Green's function for zero frequency, ii) is shown to be both ultraviolet and infrared finite.