All Questions
Tagged with mathematical-physics foundations
18
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What are the distinct mathematical formalisms of quantum mechanics?
Consider the physical theory called non-relativistic quantum mechanics. What are the distinct mathematical formalisms for this physical theory? That is, different mathematical frameworks for this ...
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What is the mathematical definition of bound state? [duplicate]
While searching why poles of Green’s function corresponds to bound states I came across that I don't know what bound state is. Intuitivaly I know that bound
State should be a state that the ...
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Can mass be defined using projective Hilbert space formalism instead of Hilbert space formalism?
The origin of mass in quantum mechanics was clarified by Bargmann in his famous paper, On Unitary Ray Representations of Continuous Groups (Annals of Mathematics, Second Series, Vol. 59, No. 1 (Jan., ...
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Non-distributivity of quantum logic according to C. Piron
I'm trying to understand this highlighted sentence in Piron's "Foundations of Quantum Physics" on p. 21:
I know that distributivity of a lattice means $a\land (b\lor c)=(a\land b)\lor(a\...
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Reference Request: Mathematical Foundations of Physics
I am looking for reading on examples, or preferably a comprehensive summary on how the foundations of mathematics are related to physical theory. I would like to know whether basic set-theoretic and ...
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Is there a foundation of mathematical logic? [duplicate]
As Mathematics has its foundations in logic and set theory in the sense that you can derive all of mathematics from such theories, does mathematical physics have such foundations? A theory or theories ...
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Can a mathematical proof replace experimentation?
I know that this is very similar to How important is mathematical proof in physics? as well as Is physics rigorous in the mathematical sense? and The Role of Rigor. However, none of the answers to ...
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Is there a reason why the subset of our Hilbert space that corresponds to a particle is a vector subspace?
I'm trying to gain some intuition behind the definition that states a particle is an irreducible unitary representation of the restricted Poincare group (or more specifically, its double cover).
Let'...
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A Spin up particle in QFT
This appears like a question that is rarely addressed in field theory pedagogy (perhaps because the answer is obvious): how does one describe a particle of definite spin in quantum field theory?
For ...
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About Hilbert and Physics [duplicate]
Was one of Hilbert questions regarding physics to make an axiomatic foundation for physics? Regardless of Godels work could some Physics principles that are 'basic' and 'presently verifiable' be ...
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What are type system examples of local gauge transformation- and field strength-like objects?
This is essentially a follow up motivated by this answer to my question about the gauge transformation interpretation of identity types.
A field
$$\psi:\mathcal M\to\mathbb C^n$$
is a section of the ...
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Are identity types interpreted physically in an infinity-topos formulation of equations of motion?
In reference to Urs Schreibers paper/book on foundations of field theory Differential cohomology in a cohesive infinity-topos I wonder: are identity types there used "only" for the computations, or ...
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What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?
I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly.
Hilbert's sixth problem consisted roughly about finding axioms for physics (...
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How important is mathematical proof in physics?
How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
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In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?
Isham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is ...
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