An eight-dimensional realization of the Clifford algebra in the five-dimensional Galilean covariant spacetime

Kobayashi, Masanori; Montigny, M. de; Khanna, F. C.

doi:10.1088/1751-8113/41/12/125402

Cited by 4 publications

(8 citation statements)

References 15 publications

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“…27 It is well known that pseudo-type interactions cannot be introduced into the ͑4+1͒-dimensional Galilean covariant theory. Let us explain this situation for the case of the solution of the Dirac-type equation in the ͑5+1͒-dimensional Galilean covariant theory.…”

Section: Discussionmentioning

confidence: 99%

A connection between spin and statistics based on Galilean invariant delta functions

Kobayashi

Montigny

Khanna

2010

Journal of Mathematical Physics

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A new Hamilton operator for a massive relativistic particle with spin one in a generalized Heisenberg/Schrödinger picture We define Galilean invariant delta functions by using the Takahashi formulation, which describes particles with arbitrary spin. The direct calculation of the Galilean invariant delta functions in the ͑N +1͒-dimensional Galilean covariant extended manifolds reveals that, for N odd, there exists a surface on which these delta functions vanish. This feature corresponds to the spacelike separation in the relativistic quantum field theory, and it enables us to discuss a connection between spin and statistics in the Galilean covariant theories. These results show that a spinstatistics connection holds for even-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with odd N Ն 5. Likewise, we observe that there is no such connection for odd-dimensional Galilean covariant extended manifolds; that is, for N-dimensional space-times with even N Ն 4. Thus, our results support the claim that there is no connection between spin and statistics in the usual nonrelativistic theory, for which N =4.

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Section: Discussionmentioning

confidence: 99%

A connection between spin and statistics based on Galilean invariant delta functions

Kobayashi

Montigny

Khanna

2010

Journal of Mathematical Physics

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“…Let us consider a galilean covariant Dirac field, Ψ(x), defined on the five-dimensional manifold G (4+1) with the galilean metric [29,30]. Then the lagrangian density for such a field is given by…”

Section: Coupled Galilean Gravity and Dirac Fieldmentioning

confidence: 99%

“…In Appendix A the representations of γ a in 4-dimension are given, for a (3+1) dimensional space-time. Let us apply the variational principle to the free Lagrangian (29). Then the Euler-Lagrange equations of motion for Ψ(x) and its adjoint Ψ(x) are respectively…”

Section: Coupled Galilean Gravity and Dirac Fieldmentioning

confidence: 99%

Teleparallel formalism of Galilean gravity

Ulhoa¹,

Khanna²,

Santana³

2011

Gravit. Cosmol.

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A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1) dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed and a galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of galilean covariant equations. In addition, this Galilei teleparallel approach provides a prescription to couple the 5-bein field to the galilean covariant Dirac field.

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“…[3]. The canonical conjugate variable of the extended coordinates in the (5+1) Galilean space-time provides a transparent interpretation of the additional parameter s. Indeed, the 6-momentum,…”

Section: Introductionmentioning

confidence: 99%

CPT theorem in a Galilean space–time

2008

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We extend the 5-dimensional Galilean space-time to a (5+1) Galilean spacetime in order to define a parity transformation in a covariant manner. This allows us to discuss the discrete symmetries in the Galilean space-time, which is embedded in the (5 + 1) Minkowski space-time. We discuss the Dirac-type field, for which we give the 8 × 8 gamma matrices explicitly. We demonstrate that the CPT theorem holds in the (5 + 1) Galilean space-time.

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An eight-dimensional realization of the Clifford algebra in the five-dimensional Galilean covariant spacetime

Cited by 4 publications

References 15 publications

A connection between spin and statistics based on Galilean invariant delta functions

A connection between spin and statistics based on Galilean invariant delta functions

Teleparallel formalism of Galilean gravity

CPT theorem in a Galilean space–time

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