E. Harikumar

We construct Maxwell and Yang-Mills theories in the rainbow space-time. We show that the time-dependent Aharonov-Bohm phases for both Abelian and non-Abelian gauge fields are non-zero in the rainbow space-time, unlike in Minkowski space-time, where they are zero. Starting from the Poisson brackets between coordinates and velocities of a massive particle moving in rainbow space-time and interacting with Abelian/non-Abelian gauge fields, we derive Maxwell's/Yang-Mills equations in rainbow space-time using a variant of Feynman's approach. In this approach, one replaces kinetic momentum with conjugate momentum and the gauge field to calculate the Poisson brackets. Finding the time-derivative of these Poisson brackets and exploiting their anti-symmetry property, a second rank anti-symmetric tensor is introduced which is the field strength associated with Maxwell/Yang-Mills theory, respectively. We show the gauge invariance/covariance of these field strengths explicitly and by demanding the gauge invariance, construct Maxwell's/Yang-Mills Lagrangians. We derive the Lorentz force equation for the particle moving in rainbow space-time in the presence of Abelian/non-Abelian gauge fields. Using the gauge field strength in rainbow space-time, expressed in terms of field strength in the Minkowski space-time and rainbow parameters, we explicitly evaluate the Aharonov-Bohm phases for different choices of rainbow functions and also for different possible gauge field configurations. We show that the time-dependent Aharonov-Bohm phases for Abelian as well as non-Abelian fields are, in general, non-zero in the rainbow space-time. The non-vanishing of time-dependent Aharonov-Bohm phase, which distinguishes rainbow space-time from Minkowski space-time, is a clear signal to be measured to validate the rainbow space-time.

We study the operator formulation of classical mechanics by explicitly applying it to two central potentials in two dimensions. After constructing the classical Hamiltonian operators and corresponding Schrödinger-like equations, we solve for the corresponding classical wave functions associated with these two potentials, viz, Kepler and harmonic potentials. While satisfying continuity equations, these classical wave functions are shown to be renormalizable only in a finite region of the 2D plane. We also derive the well-known equivalence between these two models within the operator formulation of classical mechanics. This equivalence is shown by relating the Schrödinger-like equations and corresponding classical wave functions of these two systems, using the Levi-Civita map and a reparametrization of time (Sundman map).

We construct and analyse wormhole solutions in quantised space-time. The field equations are constructed from the deformed wormhole metric in the proper reference frame using tetrads. The spatial geometry of the wormhole is analysed in kappa space-time. Further, modifications to the conditions that ensure traversibility of the wormhole are studied and it is found that the necessity of the exotic matter persists in the non-commutative case as in the commutative space-time. Casimir energy is considered a possible source for exotic matter and it is shown that the time to pass through the wormhole as well as the amount of exotic matter required to create the wormhole reduce due to non-commutativity of space-time.

We construct and analyse wormhole solutions in quantised space-time. The field equations are constructed from the deformed wormhole metric in the proper reference frame using tetrads. The spatial geometry of the wormhole is analysed in the kappa space-time. Further, the modifications to the conditions that ensure traversibility of the wormhole are studied and it is found that the necessity of the exotic matter persists in the non-commuative case as in the commutative space-time. Casimir energy is considered a possible source for exotic matter and it is shown that the time to pass through the wormhole as well as the amount of exotic matter required to create the wormhole reduce due to non-commutativity of space-time.

We investigate the implications of a fundamental length scale on the centripetal force on a rotating Casimir apparatus in $κ$-space-time. We model the Casimir apparatus rotating with constant angular speed using appropriate $κ$-deformed coordinates. We find the $κ$-deformed centripetal force on a single plate, as well as for parallel plates. We show that the Casimir energy, including the divergent part (self energies of the plates) experiences centripetal forces like a conventional mass. We also find centripetal force on oriented parallel plates rotating with constant angular speed in $κ$-space-time. Results show that the mass-energy equivalence principle holds in the $κ$-space-time.