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A new framework for deriving equations of motion for constrained quantum systems is introduced, and a procedure for its implementation is outlined. In special cases the framework reduces to a quantum analogue of the Dirac theory of…
A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be…
Divergence in perturbative expansions is where interesting physics takes place. Particle production on time-dependent backgrounds, as one such example, is interpreted as transition from one vacuum to another. Vacuum is typically defined as…
A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…
The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
Any quantum theory of gravity which treats the gravitational constant as a dynamical variable has to address the issue of superpositions of states corresponding to different eigenvalues. We show how the unobservability of such…
Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension…
We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed…
A qualitative but formalized representation of microstates is first established quite independently of the quantum mechanical mathematical formalism, exclusively under epistemological-operational-methodological constraints. Then, using this…
We demonstrate an alternative method for calculating the asymptotic behaviour of the discrete one-coin quantum walk on the infinite line, via the Jacobi polynomials that arise in the path integral representation. This is significantly…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
The higher-order WKB Mathematica code for computing quasinormal modes, whose accuracy was significantly enhanced through extensions to higher orders and, in particular, through the use of Pad\'e resummation, has been widely employed in…
We investigate some properties of the WKB series for arbitrary analytic potentials and then specifically for potentials $x^N$ ($N$ even), where more explicit formulae for the WKB terms are derived. Our main new results are: (i) We find the…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
In this paper we discuss a formulation of relativistic quantum mechanics that uses Euclidean Green functions or generating functionals as input. This formalism has a close relation to quantum field theory, but as a theory of linear…
The quark form factor is known to exponentiate within the framework of dimensionally regularized perturbative QCD. The logarithm of the form factor is expressed in terms of integrals over the scale of the running coupling. I show that these…
In the first part of this thesis we study the generalization of the recent algebraic approach to classical field theory by proposing a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…