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Research paper thumbnail of Off-shell Supersymmetric Continuous Spin Gauge Theory

We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-d... more We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1], we employ an auxiliary field to close the algebra of supersymmetry transformations off-shell. The 4d N = 1 massless continuous spin supermultiplet is then denoted by (Φ, H ; Ψ), comprised of a dynamical and a non-dynamical complex scalar continuous spin gauge fields Φ and H, as well as a Dirac continuous spin gauge field Ψ. In particular, we demonstrate that the continuous spin super-multiplet, in a limit, reproduces off-shell supersymmetry transformations of the known scalar (chiral) supermultiplet (0 , 1/2), all integer-spin supermultiplets (s , s + 1/2), s 1, and all half-integer spin supermultiplets (s − 1/2 , s), s 1.

Papers by Mojtaba Najafizadeh

Research paper thumbnail of Supersymmetric Continuous Spin Gauge Theory: off-shell formulation

Research paper thumbnail of Interactions of continuous spin particle (CSP) with matter

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas, and the 3-dimensional harmonic oscillator.

Research paper thumbnail of Modified Wigner equations and continuous spin gauge field

In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous ... more In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in A(dS) spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.

Research paper thumbnail of Off-shell supersymmetric continuous spin gauge theory

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas and the 3-dimensional harmonic oscillator.

Research paper thumbnail of Unconstrained Massless Higher Spin Supermultiplet in AdS$_4$

We consider unconstrained formulation of the higher spin gauge theory in anti-de Sitter (AdS) spa... more We consider unconstrained formulation of the higher spin gauge theory in anti-de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for theN = 1 unconstrained massless higher spin supermultiplet in four-dimensional AdS4. Such an irreducible supermultiplet (Φ1,Φ2 ; Ψ1,Ψ2) contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank s = 0, 1, . . . ,∞), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin s = 1 2 , 3 2 , . . . ,∞).

Research paper thumbnail of Supersymmetric continuous spin gauge theory

Journal of High Energy Physics

Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supe... more Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the N = 1 supermultiplet in four-dimensional flat space-time, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its superpartner which can be called " CSPino " is considered to be a Dirac continuous spin field. It is shown that the algebra of these supersymmetry transformations are closed on-shell. Furthermore, we investigate whether obtained supersymmetry transformations reproduce the known result of the higher spin gauge field theory in the helicity limit. Finally, we illustrate how these two separate set of obtained transformations are related to each other.

Research paper thumbnail of Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes

Physical Review D

Building on Segal's local free action principle for bosonic unconstrained higher spin gauge field... more Building on Segal's local free action principle for bosonic unconstrained higher spin gauge fields in d-dimensional ðAÞdS d spacetime, we present a similar action principleà la Segal for fermions in d-dimensional ðAÞdS d spacetime. Moreover, at the level of equations of motion, we demonstrate how the Fronsdal and the Fang-Fronsdal equations in d-dimensional ðAÞdS d spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.

Research paper thumbnail of Modified Wigner equations and continuous spin gauge field

Physical Review D

In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous ... more In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in (A)dS spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.

Research paper thumbnail of Continuous-spin field propagator and interaction with matter

Journal of High Energy Physics

Action principles for the single and double valued continuous-spin representations of the Poincar... more Action principles for the single and double valued continuous-spin representations of the Poincaré group have been recently proposed in a Segal-like formulation. We address three related issues: first, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.

Research paper thumbnail of A gauge field theory of fermionic continuous-spin particles

Physics Letters B

In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continu... more In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas and the 3-dimensional harmonic oscillator.

Research paper thumbnail of Off-shell Supersymmetric Continuous Spin Gauge Theory

We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-d... more We construct, for the first time, an off-shell supersymmetric continuous spin gauge theory in 4-dimensional Minkowski spacetime, in both constrained and unconstrained Lagrangian formulations. As an extension to the on-shell description [1], we employ an auxiliary field to close the algebra of supersymmetry transformations off-shell. The 4d N = 1 massless continuous spin supermultiplet is then denoted by (Φ, H ; Ψ), comprised of a dynamical and a non-dynamical complex scalar continuous spin gauge fields Φ and H, as well as a Dirac continuous spin gauge field Ψ. In particular, we demonstrate that the continuous spin super-multiplet, in a limit, reproduces off-shell supersymmetry transformations of the known scalar (chiral) supermultiplet (0 , 1/2), all integer-spin supermultiplets (s , s + 1/2), s 1, and all half-integer spin supermultiplets (s − 1/2 , s), s 1.

Research paper thumbnail of Supersymmetric Continuous Spin Gauge Theory: off-shell formulation

Research paper thumbnail of Interactions of continuous spin particle (CSP) with matter

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas, and the 3-dimensional harmonic oscillator.

Research paper thumbnail of Modified Wigner equations and continuous spin gauge field

In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous ... more In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in A(dS) spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.

Research paper thumbnail of Off-shell supersymmetric continuous spin gauge theory

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas and the 3-dimensional harmonic oscillator.

Research paper thumbnail of Unconstrained Massless Higher Spin Supermultiplet in AdS$_4$

We consider unconstrained formulation of the higher spin gauge theory in anti-de Sitter (AdS) spa... more We consider unconstrained formulation of the higher spin gauge theory in anti-de Sitter (AdS) spacetime, given by actions [1, 2], and provide on-shell supersymmetry transformations for theN = 1 unconstrained massless higher spin supermultiplet in four-dimensional AdS4. Such an irreducible supermultiplet (Φ1,Φ2 ; Ψ1,Ψ2) contains a pair of bosonic fields, with opposite parity, which are generating functions (infinite collection of totally symmetric real tensor fields of all integer rank s = 0, 1, . . . ,∞), as well as two fermionic fields, which have opposite signs of the AdS radius, that are spinorial generating functions (infinite tower of totally symmetric Majorana spinor-tensor fields of all half-integer spin s = 1 2 , 3 2 , . . . ,∞).

Research paper thumbnail of Supersymmetric continuous spin gauge theory

Journal of High Energy Physics

Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supe... more Taking into account the Schuster-Toro action and its fermionic analogue discovered by us, we supersymmetrize unconstrained formulation of the continuous spin gauge field theory. Afterwards, building on the Metsaev actions, we supersymmetrize constrained formulation of the theory. In each formulation, we provide supersymmetry transformations for the N = 1 supermultiplet in four-dimensional flat space-time, in which continuous spin particle (CSP) is considered to be a complex scalar continuous spin field, and its superpartner which can be called " CSPino " is considered to be a Dirac continuous spin field. It is shown that the algebra of these supersymmetry transformations are closed on-shell. Furthermore, we investigate whether obtained supersymmetry transformations reproduce the known result of the higher spin gauge field theory in the helicity limit. Finally, we illustrate how these two separate set of obtained transformations are related to each other.

Research paper thumbnail of Local action for fermionic unconstrained higher spin gauge fields in AdS and dS spacetimes

Physical Review D

Building on Segal's local free action principle for bosonic unconstrained higher spin gauge field... more Building on Segal's local free action principle for bosonic unconstrained higher spin gauge fields in d-dimensional ðAÞdS d spacetime, we present a similar action principleà la Segal for fermions in d-dimensional ðAÞdS d spacetime. Moreover, at the level of equations of motion, we demonstrate how the Fronsdal and the Fang-Fronsdal equations in d-dimensional ðAÞdS d spacetime are related, respectively, to the Euler-Lagrange equations of the bosonic and fermionic higher spin actions mentioned above.

Research paper thumbnail of Modified Wigner equations and continuous spin gauge field

Physical Review D

In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous ... more In this paper, we first propose the bosonic (fermionic) modified Wigner equations for continuous spin particle (CSP). Secondly, starting from the (Fang-)Fronsdal-like equation, we will reach to the modified action of bosonic (fermionic) continuous spin gauge field in flat spacetime, presented recently by Metsaev in (A)dS spacetime. We shall also explain how to obtain the proposed modified Wigner equations from the gauge-fixed equations of motion. Finally, we will consider the massive bosonic (fermionic) higher-spin action and, by taking the infinite spin limit, we will arrive at the modified bosonic (fermionic) CSP action.

Research paper thumbnail of Continuous-spin field propagator and interaction with matter

Journal of High Energy Physics

Action principles for the single and double valued continuous-spin representations of the Poincar... more Action principles for the single and double valued continuous-spin representations of the Poincaré group have been recently proposed in a Segal-like formulation. We address three related issues: first, we explain how to obtain these actions directly from the Fronsdal-like and Fang-Fronsdal-like equations by solving the traceless constraints in Fourier space. Second, we introduce a current, similar to the one of Berends, Burgers and Van Dam, which is bilinear in a pair of scalar matter fields, to which the bosonic continuous-spin field can couple minimally. Third, we investigate the current exchange mediated by a continuous-spin particle obtained from this action principle and investigate whether it propagates the right degrees of freedom, and whether it reproduces the known result for massless higher-spin fields in the helicity limit.

Research paper thumbnail of A gauge field theory of fermionic continuous-spin particles

Physics Letters B

In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continu... more In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang-Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

Research paper thumbnail of Thermodynamics of Classical Systems on Noncommutative Phase Space

We study the formulation of statistical mechanics on noncommutative classical phase space, and co... more We study the formulation of statistical mechanics on noncommutative classical phase space, and construct the corresponding canonical ensemble theory. For illustration, some basic and important examples are considered in the framework of noncommutative statistical mechanics: such as the ideal gas, the extreme relativistic gas and the 3-dimensional harmonic oscillator.