Journal ArticleDOI
Feynman path integrals. I. Linear and affine techniques. II. The Feynman-Green function
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This article is published in Communications in Mathematical Physics.The article was published on 1974-03-01. It has received 53 citations till now. The article focuses on the topics: Feynman slash notation & Feynman diagram.read more
Citations
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Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
TL;DR: In this article, a quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphicism constraint is solved and the space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions.
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Projective techniques and functional integration for gauge theories
Abhay Ashtekar,Jerzy Lewandowski +1 more
TL;DR: In this paper, a general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces, then applied to gauge theories to carry out integration over the non-linear, infinite-dimensional spaces of connections modulo gauge transformations.
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Path integration in non-relativistic quantum mechanics
TL;DR: In this paper, path integrals for path on curved spaces and for paths on multiply-connected spaces are computed explicitly and applied to problems in nonrelativistic quantum mechanics, such as wave functions, propagators on configuration spaces and on phase space, caustic problems, bound states.
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The semiclassical expansion
TL;DR: In this article, a new definition of path integrals is given to compute the semiclassical expansion of the probability amplitude of a transition A → B K(B; A) = K o (B, A) ∑ n=o ∞ (iℏ) n A n.
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A new perspective on functional integration
TL;DR: In this article, a general theorem with a large number of specializations was proved for a manifold N and a finite number of one-parameter groups of point transformations on N with generators Y,X(1),..., X(d), Y(2,1), X(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,
References
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Book
Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
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The Correspondence Principle in the Statistical Interpretation of Quantum Mechanics
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On the Definition and Approximation of Feynman's Path Integrals
TL;DR: In this paper, a general and compact expression for Feynman's path integral has been obtained and a classical method for the computation of such expressions is given for the Dirac particle in a constant external electromagnetic field.
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Feynman's path integral. definition without limiting procedure
TL;DR: In this article, Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, if C is the topological dual of C, then C can be written as
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The wiener integral
TL;DR: In this article, the Fourier-Wiener transform is used to define the Wiener integral and integral equations, and the indefinite Wiener transform can be used to approximate the approximate evaluation of continuous integrals.