Related papers: Path integration and perturbation theory with comp…
Witten constructed a topological quantum field theory with the Chern-Simons action as Lagrangian. We define a Chern-Simons action for 3-dimensional spectral triples. We prove gauge invariance of the Chern-Simons action, and we prove that it…
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…
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…
Path integrals constitute powerful representations for both quantum and stochastic dynamics. Yet despite many decades of intensive studies, there is no consensus on how to formulate them for dynamics in curved space, or how to make them…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
The path decomposition expansion represents the propagator of the irreversible reaction as a convolution of the first-passage, last-passage and rebinding time probability densities. Using path integral technique, we give an elementary, yet…
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…
We study the path-integral formalism in the imaginary-time to show its validity in a case with a metastable ground state. The well-known method based on the bounce solution leads to the imaginary part of the energy even for a state that is…
The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field…
Using the Ashtekar formulation, it is shown that the G_{Newton} --> 0 limit of Euclidean or complexified general relativity is not a free field theory, but is a theory that describes a linearized self-dual connection propagating on an…
On the basis of the canonical quantization procedure, in which we need the indefinite metric Hilbert space, we formulate field diagonal representation for the scalar Lee-Wick model. Euclidean path integral for the model is then constructed…
It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical…
Polyakov's spin factor enters as a weight in the path-integral description of particle-like modes propagating in Euclidean space-times, accounting for particle spin. The Fock-Feynman-Schwinger path integral applied to QCD accomodates…
Quantum tunneling in a many-body system is much more non-trivial than that in a one-body system. The most characteristic phenomenon is the mixed tunneling, which has been studied in many fields for decades. For instance, let us consider a…
Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of the method of Feynman diagrams. In…
Minkowski spacetime can be mapped by a series of projections in a higher-dimensional spacetime to a Euclidean space, constituting a process of Euclideanization shown here in detail for two dimensions. The result allows regularizations and…
This paper derives the Feynman rules for the diagrammatic perturbation expansion of the effective action around an arbitrary solvable problem. The perturbation expansion around a Gaussian theory is well known and composed of one-line…
Two long-standing problems in the construction of coherent state path integrals, the unwarranted assumption of path continuity and the ambiguous definition of the Hamiltonian symbol, are rigorously solved. To this end the fully controlled…