Operations and effects in the Hilbert space formulation of quantum theory

2008 ◽  
pp. 206-229 ◽  
Author(s):  
K. Kraus
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Space Formulation

scholarly journals Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory

10.14311/1195 ◽  
2010 ◽  
Vol 50 (3) ◽  
Author(s):  
M. Znojil
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Hilbert Spaces ◽  
Nuclear Physics ◽  
Bound State ◽  
Wave Functions ◽  
Time Dependent ◽  
Moving Frame ◽  
Standard Textbook ◽  
Space Formulation

A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics) is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian”) Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models) is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S) of the standard physical Hilbert space of wave functions.

Functional Quantum Theory of Free Relativistic Fermi Fields

1970 ◽  
Vol 25 (5) ◽  
pp. 575-586
Author(s):  
H. Stumpf
Keyword(s):  
Hilbert Space ◽  
Quantum Theory ◽  
Physical Interpretation ◽  
Functional Equations ◽  
Dirac Field ◽  
Functional Hilbert Space ◽  
Free Fermi ◽  
Special Case ◽  
Relativistic Fermi

Functional quantum theory of free Fermi fields is treated for the special case of a free Dirac field. All other cases run on the same pattern. Starting with the Schwinger functionals of the free Dirac field, functional equations and corresponding many particle functionals can be derived. To establish a functional quantum theory, a physical interpretation of the functionals is required. It is provided by a mapping of the physical Hilbert space into an appropriate functional Hilbert space, which is introduced here. Mathematical details, especially the problems connected with anticommuting functional sources are treated in the appendices.

scholarly journals Space-time from Collapse of the Wave-function

2019 ◽  
Vol 74 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Quantum Theory ◽  
Minkowski Space ◽  
Time Scales ◽  
Quantum Interference ◽  
Quantum Dynamics ◽  
Space Time ◽  
Minkowski Space Time ◽  
Macroscopic Objects

AbstractWe propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then propose such a formulation by invoking an operator Minkowski space-time on the Hilbert space. We suggest relativistic spontaneous localisation as the mechanism for recovering classical space-time from the underlying theory. Quantum interference in time could be one possible signature for operator time, and in fact may have been already observed in the laboratory, on attosecond time scales. A possible prediction of our work seems to be that interference in time will not be seen for ‘time slit’ separations significantly larger than 100 attosecond, if the ideas of operator time and relativistic spontaneous localisation are correct.

scholarly journals Quantum Theory in Pseudo-Hilbert Space. II

1959 ◽  
Vol 21 (5) ◽  
pp. 727-730 ◽  
Author(s):  
Gaku Konisi ◽  
Takesi Ogimoto
Keyword(s):  
Hilbert Space ◽  
Quantum Theory
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