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Yes, one traditional alternative to the path integral formalism is the operator formalism. For QED with abelian gauge group, the old quantization formulation is the Gupta-Bleuler formulation. For QCD/Yang-Mills theory with non-abelian gauge group, the Gupta-Bleuler formulation is replaced by the BRST formulation. The BRST formulation exists in at least 3 ...


1

In the particle-physics-oriented part of the theoretical physics community, it was becoming increasingly clear that the Dirac bracket is at most a complicated piece of formalism that isn't able to solve any real physical problems and make theories well-defined or finite or renormalizable etc. So the people who are playing with such tools applied to ...


3

Avoiding mathematical formulae to the maximum, and warning for furious hand-waving ahead, I would state it like this: In the classical picture, there is no quanta concept, so you could have just a little bit of radiation energy at any frequency. However, since quantization appeared, the minimum amount of radiation energy that you could possibly have at a ...


1

I think you misunderstand the ultraviolet catastrophe. It does not mean that the energy radiated reaches zero at any finite frequency, just that the power tends to zero as the frequency tends to infinity. Pre-quantum physics thought that blackbody radiation was ruled by the Rayleigh-Jeans law $$ B_\nu(T) = \frac{2\nu^2 k T}{c^2} $$ This does obviously not ...


2

IMHO, in the prof Slavnov article, the action path integral formula $(3)$ for $S$ should be understood with constraints about initial and final states. So, in fact, it is a matrix $S_{ij}$. However, this is not the case for the formula $(4)$ for $Z[J]$. It is a path integral without constraints. For your second question, just note that $e^{i (S+\delta ...


0

For your question 1.: note that the integral in $Z[J]$ is performed over only paths connecting the initial state $q_i$ to the final state $q_f$, i.e., $Z[J]$ actually depends on $q_i$ and $q_f$. So, you can view it as a matrix element of $\hat{S}$, namely, $S_{ij}$.



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