Dirac operator, bicovariant differential calculus and gauge theory on -Minkowski space

Bibikov, P. N.

doi:10.1088/0305-4470/31/30/010

Cited by 8 publications

(7 citation statements)

References 16 publications

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“…Other than this transformation parameter, the information about the κ-deformation is contained only in the explicit expression of the energy ω and ω ′ appearing in Eqns. (23,24). Now we show that the Dirac field given in Eqn.…”

Section: κ-Deformed Dirac Equation and It's Solutionmentioning

confidence: 67%

“…These creation and annihilation operators satisfying the o-product rule are the ones appearing in the mode decomposition of fermionic field (see Eqns. (23,24)) satisfying the κ-deformed Dirac Eqn. (22).…”

Section: Twisted Dirac Oscillator Algebramentioning

confidence: 99%

“…But the square of the κ-Dirac equation obtained in [20] was related to the κ-deformed Pauli-Lubanski vector in contrast to the situation in commutative space-time. Using other approaches the Dirac equation in κ-space-time was constructed and studied in [21,22,23,24,25,26,27]. In this paper, we use κ-Dirac equation obtained in [28], which is invariant under the undeformed κ-Poincare algebra.…”

Section: Introductionmentioning

confidence: 99%

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Twisted fermionic oscillator algebra in κ-minkowski space-time

Verma

2015

Eur. Phys. J. Plus

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In this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in κ-Minkowski spacetime. Starting from κ-deformed Dirac theory, which is invariant under the undeformed κ-Poincare algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in κ-Minkowski space-time. In the limit a →0, the deformed algebra reduces to the commutative result. *

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Section: κ-Deformed Dirac Equation and It's Solutionmentioning

confidence: 67%

Section: Twisted Dirac Oscillator Algebramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Twisted fermionic oscillator algebra in κ-minkowski space-time

Verma

2015

Eur. Phys. J. Plus

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“…By using this κ-Dirac equation, the modification of the Unruh effect was studied in [13] (and for scalar field this was studied in [14]). The Dirac equation in κ-deformed space-time was constructed and analysed by using different approaches in [15,16,17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Dirac Equation in $κ$-Minkowski space-time

Verma

2014

Preprint

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In this paper, we derive the Dirac equation in the κ-deformed Minkowski space-time. We start with κ-deformed Minkowski spacetime and investigate the undeformed κ-Lorentz transformation valid to all order in the deformation parameter a. Using the undeformed κ-Lorentz algebra, we obtain the κ-deformed Dirac equation, valid to all order in the deformation parameter a. In limit a →0, we get back the correct commutative result.

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“…But, the anti-particle equation consistent with deformed special relativity was shown to be different from the same on κ-spacetime. Some other approaches towards the construction of Dirac equation on κ-spacetime were attempted in [58][59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Κ-Deformed DIRAC EQUATION

2011

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In this paper we study the quantisation of Dirac field theory in the κ-deformed space-time. We adopt a quantisation method that uses only equations of motion for quantising the field. Starting from κ-deformed Dirac equation, valid up to first order in the deformation parameter, we derive deformed unequal time anti-commutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anti-commutation relations between κ-deformed spinor and its conjugate, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the κ-deformed conserved currents, valid up to first order in a, corresponding to parity and time-reversal symmetries of κ-deformed Dirac equation. a fundamental length scale. DSR is also known to modify the energy-momentum dispersion relation. It has been shown in [8], that the symmetry algebra of the κ-deformed space-time is defined by the κ-Poincare algebra, which is a Hopf algebra. The symmetry algebra of the κ-deformed space-time can also be realised using undeformed κ-Poincare algebra, where the defining relations are same as that of the usual Poincare algebra, but then the explicit form of the generators are deformed [9][10][11][12][13].Various studies have been carried out analysing field theory models defined in κ-deformed spacetime [14][15][16][17][18][19][20][21][22][23][24]. In most of these studies, field equations, which are invariant under the symmetry algebra, defined in κ-deformed space-times are set up from the κ-deformed quadratic Casimir [9] of the algebra. Since the quadratic Casimir has higher-order derivatives, the Lagrangian corresponding to these deformed field equations also contains higher-order derivative terms in it, signalling the non-local nature of the non-commutative field theories and make canonical quantisation difficult.The knowledge of the explicit form of the Lagrangian is necessary for applying the canonical scheme to quantise field theory, but there exists an alternate quantisation procedure which does not require the Lagrangian for quantising field theories. Instead, this method uses the equations of motion of the field theory as the starting point for the quantisation [25][26][27]. The quantisation of massive spin-one field has been studied using this method [28]. In [29] covariant commutation relation for field describing an arbitrary spin had been obtained using this method. In this method, every free field equation of motion is converted to Klein-Gordon equation with the help of an operator called Klein-Gordon divisor [25][26][27]. This Klein-Gordon divisor is then used to define an unequal time anti-commutation relation between the spinor field operator and its adjoint operator such that the field equations are consistent with the Heisenberg's equations of motion and it leads to the usual (anti-) commutation relations between the creation and annihilation ...

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Dirac operator, bicovariant differential calculus and gauge theory on -Minkowski space

Cited by 8 publications

References 16 publications

Twisted fermionic oscillator algebra in κ-minkowski space-time

Twisted fermionic oscillator algebra in κ-minkowski space-time

Dirac Equation in $κ$-Minkowski space-time

Κ-Deformed DIRAC EQUATION

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