Related papers: Path Intergals and Perturbative Expansions for Non…
I address and solve the natural problem of calculating the transverse current anomalies in quantum electrodynamics by means of the path-integral method. An explicitly divergent and regulator-dependent anomaly term is produced for the vector…
We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of $d$, $N\times N$ matrices invariant under the adjoint action of the symmetric…
The structure of supersymmetry is analyzed systematically in ${\cal PT}$ symmetric quantum mechanical theories. We give a detailed description of supersymmetric systems associated with one dimensional ${\cal PT}$ symmetric quantum…
A complete perturbative expansion for the Hamiltonian describing the motion of a quantomechanical system constrained to move on an arbitrary submanifold of its configuration space $R^n$ is obtained.
Representations of propagators by means of path integrals over velocities are discussed both in nonrelativistic and relativistic quantum mechanics. It is shown that all the propagators can only be expressed through bosonic path integrals…
We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a new functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As…
Recent developments in holographic gravity suggest that spacetime structure may be deeply related to quantum mechanics. In this work, from a different perspective, we demonstrate that wave-particle duality can be interpreted as the…
We study a pathwise integral with respect to paths of finite quadratic variation, defined as the limit of non-anticipative Riemann sums for gradient-type integrands. We show that the integral satisfies a pathwise isometry property,…
The unitary transformation of path-integral differential measure is described. The main properties of perturbation theory in the phase space of action-angle, energy-time variables are investigated. The measure in cylindrical coordinates is…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the…
We introduce, for the first time, bicoherent-state path integration as a method for quantizing non-hermitian systems. Bicoherent-state path integrals arise as a natural generalization of ordinary coherent-state path integrals, familiar from…
In the path integral formulation of the partition function of quantum spin models, most current treatments employ the so-called static approximation to simplify the process of summing over all possible paths. Although sufficient for…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
A new path integral approach of quantum gravity based on relational variables and quantum test objects is presented. We take as a basic variables the squared invariant distance. This invariant quantity is technically simpler to work with…
A path-integral approach to non-perturbative topological invariants of knots, links and manifolds of dimension three and four using topological quantum field theory of Schwarz (Chern-Simons) type is presented.
For many years coherent states have been a useful tool for understanding fundamental questions in quantum mechanics. Recently, there has been work on developing a consistent way of including constraints into the phase space path integral…
We present a path integral formalism for quantising gravity in the form of the spectral action. Our basic principle is to sum over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries: the…
In these notes, we elucidate some subtle aspects of coherent-state path integrals, focusing on their application to the equilibrium thermodynamics of quantum many-particle systems. These subtleties emerge when evaluating path integrals in…
The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra…