As a First step, I am reading this paper...
arXiv:hep-th/9302097 [pdf, ps, other]
Title: An Introduction into the Feynman Path Integral
Authors: Christian Grosche
Comments: 92 pages, amstex, Leipzig University preprint NTZ Nr.29/92
Subjects: High Energy Physics - Theory (hep-th)
after, I'd like to read some more papers like :
Title: The formal path integral and quantum mechanics
Authors: Theo Johnson-Freyd
Comments: 33 pages, many TikZ diagrams, submitted to _Journal of Mathematical Physics_
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)
Timeless path integral for relativistic quantum mechanics
Authors: Dah-Wei Chiou
(Submitted on 28 Sep 2010)
Abstract: Starting from the canonical formalism of relativistic (timeless) quantum mechanics, the formulation of timeless path integral is rigorously derived. The transition amplitude is reformulated as the sum, or functional integral, over all possible paths in the constraint surface specified by the (relativistic) Hamiltonian constraint, and each path contributes with a phase identical to the classical action divided by $\hbar$. The timeless path integral manifests the timeless feature as it is completely independent of the parametrization for paths. For the special case that the Hamiltonian constraint is a quadratic polynomial in momenta, the transition amplitude admits the timeless Feynman's path integral over the (relativistic) configuration space.
| Comments: | 30 pages |
| Subjects: | General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph) |
| Cite as: | arXiv:1009.5436v1 [gr-qc] |
Path Integral Quantization of Generalized Quantum Electrodynamics
(Submitted on 18 Aug 2010 (v1), last revised 14 Feb 2011 (this version, v2))
Abstract: In this paper, a complete covariant quantization of generalized electrodynamics is shown through the path integral approach. To this goal, we first studied the hamiltonian structure of system following Dirac's methodology and, then, we followed the Faddeev-Senjanovic procedure to obtain the transition amplitude. The complete propagators (Schwinger-Dyson-Fradkin equations) of the correct gauge fixation and the generalized Ward-Fradkin-Takahashi identities are also obtained. Afterwards, an explicit calculation of one-loop approximation of all Green's functions and a discussion about the obtained results are presented.
| Comments: | 25 pages, 5 figures |
| Subjects: | High Energy Physics - Theory (hep-th) |
| Journal reference: | Phys.Rev.D83:045007,2011 |
| DOI: | 10.1103/PhysRevD.83.045007 |
| Cite as: | arXiv:1008.3181v2 [hep-th] |
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