相关论文: Path integrals and boundary conditions
Recently, there were works claiming that path integral quantisation of gauge theories necessarily requires relaxation of Lagrangian constraints. As has also been noted in the literature, it is of course wrong since there perfectly exist…
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
The Feynman path integral plays a crucial role in quantum mechanics, offering significant insights into the interaction between classical action and propagators, and linking quantum electrodynamics (QED) with Feynman diagrams. However, the…
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…
Given an arbitrary Lagrangian function on \RR^d and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by "Feynman diagrams," although these…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
The Feynman path integral approach to quantum mechanics is examined in the case where the configuration space is curved. It is shown how the ambiguity that is present in the choice of path integral measure may be resolved if, in addition to…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the…
A path integral formalism for non-equilibrium systems is proposed based on a manifold of quasi-equilibrium densities. A generalized Boltzmann principle is used to weight manifold paths with the exponential of minus the information…
I offer some historical comments about the origins of Feynman's path integral approach, as an alternative approach to standard quantum mechanics. Looking at the interaction between Einstein and Feynman, which was mediated by Feynman's…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2\pi\hbar/T$, where $T$ is the typical…
The Feynman path integral is defined over the space $\mathbb{R}^T$ of all possible paths; it has been a powerful tool to develop Quantum Mechanics. The absolute value of Feynman's integrand is not integrable, then Lebesgue integration…
The very early universe is understood in terms of quantum field theories on curved spacetime, where the classical background spacetime is typically an FLRW cosmology and the quantum fields which propagate on it include gravitational waves…
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…
With this paper, a consistent and comprehensive treatise on the foundations of the extended Hamilton-Lagrange formalism will be presented. In this formalism, the system's dynamics is parametrized along a system evolution parameter $s$, and…
Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…