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Learn the Basics of Hilbert Spaces and Their Relatives: Definitions Hilbert spaces are at first real or complex vector spaces, or are Hilbert spaces So all the theorems and definitions of linear algebra apply to the finite-dimensional ones and many to the infinite-dimensional ones, and we start at known ground
The History and Importance of the Riemann Hypothesis David Hilbert and Pólya György had already noticed that the Riemann hypothesis would follow if the zeros were eigenvalues of an operator where is a Hermitian (i e self-adjoint) operator, which therefore has only real eigenvalues, similar to the Hamiltonian operators in quantum mechanics
Derivation of the Einstein-Hilbert Action - Physics Forums Derivation of the Einstein-Hilbert Action Abstract Most people justify the form of the E-H action by saying that it is the simplest scalar possible But simplicity, one can argue, is a somewhat subjective and ill-defined criterion Also, simplicity does not shed light on the axiomatic structure of general relativity
Hilbert spaces and quantum operators being infinite dimensional . . . The discussion centers on the realization that quantum operators X and P are not simple infinite-dimensional matrix generalizations, leading to the understanding that the space of quantum states is a "rigged" Hilbert space rather than a standard Hilbert space The original poster expresses confusion over manipulating these operators and seeks recommendations for rigorous yet practical
Dimensions of Hilbert Spaces confusion - Physics Forums If I understand it, Hilbert spaces can be finite (e g , for spin of a particle), countably infinite (e g , for a particle moving in space), or uncountably infinite (i e , non-separable, e g , QED) I am wondering about variations on this latter The easiest uncountable to imagine is the