Related papers: Finsler Geometrical Path Integral
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
The logical consistency of a description of Quantum Theory in the context of General Relativity, which includes Minimal Coupling Principle, is analyzed from the point of view of Feynman's formulation in terms of path integrals. We will…
The Feynman path integral for nonrelativistic quantum electrodynamics is studied mathematically of a standard model in physics, where the electromagnetic potential is assumed to be periodic with respect to a large box and quantized thorough…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of…
Suppose we have two nonequivalent but s-equivalent Lagrange functions, the question arises: are they both equally well fitted for the Feynman quantization procedure or do they lead to two different quantization schemes.
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We provide a detailed exposition of the connections between Boltzmann machines commonly utilized in machine learning problems and the ideas already well known in quantum statistical mechanics through Feynman's description of the same. We…
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
We show how to construct path integrals for quantum mechanical systems where the space of configurations is a general non-compact symmetric space. Associated with this path integral is a perturbation theory which respects the global…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
The restricted Feynman path integrals (RFPIs) have been proposed to study continuous quantum measurements in physics. The RFPIs are heuristically determined in terms of the usual probability amplitude multiplied by weight for each path,…
In nuclear and particle physics one is often faced with problems where perturbation theory is not applicable. An example of this is the description of bound states. Therefore, an exact solution of field theory to all orders is an…
Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…
We propose a path integral formulation for scale invariant quantum field theories. We do it by modifying the functional integration measure in such a way that the partition function is always exactly scale invariant, at the cost of having…
We present a computation of the coherent state path integral for a generic linear system using ``functional methods'' (as opposed to discrete time approaches). The Gaussian phase space path integral is formally given by a determinant built…
In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism.
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…