Abstract
We study the problem of stability in Podolsky's generalized electrodynamics by constructing a series of 2-parametric bounded conserved quantities. In this way, we show that the 00-component of the energy-momentum tensors could be positive definite and therefore the higher derivative system is considered to be stable. Afterwards, we derive the consistent interactions in Podolsky's theory within the framework of Hamiltonian BRST-invariant deformation procedure. The key ingredients in our analysis are the local BRST-cohomology which plays a crucial role in the determination of the first-order deformation as well as the Jacobi identity that will greatly simplify the calculations for us. We assert that in our discussions, the second-order deformation and the other higher order deformations of the BRST charge naturally turn out to be zero while the third-order as well as the corresponding higher order BRST-invariant Hamiltonian deformations also vanish completely. Moreover, we evaluate the path integral of the higher derivative constrained system before and after deformation process following the standard BRST quantization method with appropriate gauge-fixing fermions.
Highlights
Stability and consistent interactions in Podolsky’s generalized electrodynamics symplectic formalism shows to be more economical compared to the Dirac’s quantization scheme which avoids the unnecessary calculations and classification of the constraints in the quantization of gauge systems
The other higher order deformation terms can be determined by a straightforward computation following the way we derive the first- and second- order deformation and the procedure will be terminated at the fourth-order deformation. Adding up all these pieces together, we will gain the desired deformed BV action of the original Lagrangian and the antighost number zero part of this action can be interpreted as non-Abelian version of the generalized electrodynamics in the fundamental representation of some Lie algebra endowed with non-Abelian gauge symmetries
We investigate the stability of Podolsky’s generalized electrodynamics with the aid of a series of conserved quantities including the standard canonical energy-momentum tensors in the higher derivative theory
Summary
Let us turn the attentions to the calculations of the number of physical degrees of freedom of the resulting interacting theory (3.50) and we proceed using the standard Ostrogradski formalism. To implement this method, for the components of every index a, we define the corresponding canonical momenta for the independent dynamical variables (Aaμ, Γaμ = Aaμ) πμa = ∂L − ∂ν ∂L ,. After a straightforward computation, we get πia = F i0 + 1 DiDλF λ0 − 1 D0DλF λi, m2 φia = 1 DλF λi, m2. A usual Legendre transform immediately yields the canonical Hamiltonian in the form of. =tr d3x(π0Γ0 + πiΓi + φi( m2 φi + DiΓ0 + DjFij + 2g [A0, Γi] − g [A0, ∂iA0 + g [A0, Ai]]) 2
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