why not a new approach to quantum mechanics

In the decades after the discovery of general relativity it was realized that general relativity is incompatible with quantum mechanics.^[16] It is possible to describe gravity in the framework of quantum field theory like the other fundamental forces, such that the attractive force of gravity arises due to exchange of virtual gravitons, in the same way as the electromagnetic force arises from exchange of virtual photons.^[17][18] This reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length,^[16] where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required.

My reading list on PI

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 :

 

arXiv:1004.4305 [pdf, ps, other]

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

Authors: Rodrigo Bufalo, Bruto Max Pimentel, German Enrique Ramos Zambrano

(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]

\bf Euler-Lagrange \rm equation

\begin{eqnarray}
{d \over dt} {\partial L \over \partial \dot{q}_i} - {\partial L \over
\partial q_i} = 0 \label{eq:eulerlagrange}
\end{eqnarray}