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94 votes
1 answer
11k views

The mathematical theory of Feynman integrals

It is well known that Feynman integrals are one of the tools that physicists have and mathematicians haven't, sadly. Arguably, they are the most important such tool. Briefly, the question I'd like to ...
algori's user avatar
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10 votes
2 answers
2k views

Why does Riesz's Representation Theorem apply in quantum mechanics?

$\DeclareMathOperator\tr{tr}$One begins with a quantum mechanical system, i.e. a unital $C^*$-algebra $A$. It is common to begin the discussion with embedding $A$ into the algebra of bounded operators ...
Andrew NC's user avatar
  • 2,071
1 vote
1 answer
505 views

Gaussian measures on non-separable spaces

Let $X$ be a topological affine space which is neither separable nor metrizable. There are plenty of trivial Gaussian measures: each Dirac point-mass $\delta_x$ are the Gaussian measure with zero ...
Tom LaGatta's user avatar
  • 8,512