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Hidden Topological Angles in Path Integrals.

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We discovered hidden topological angles (HTAs) in quantum systems, distinct from standard parameters. These angles explain phenomena like gluon condensate vanishing and differences in quantum mechanical expansions.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Quantum Mechanics

Background:

  • Topological angles are crucial in quantum field theories and mechanical systems.
  • Understanding their origin and effects is key to advancing quantum physics.
  • Existing models do not fully account for certain quantum phenomena.

Purpose of the Study:

  • To demonstrate the existence of hidden topological angles (HTAs) in quantum field theories and quantum mechanical systems.
  • To elucidate the distinct nature of HTAs compared to Lagrangian theta parameters.
  • To explain the microscopic mechanism behind the vanishing of the gluon condensate.

Main Methods:

  • Analyzing saddle points of the complexified path integral and their descent manifolds (Lefschetz thimbles).
  • Employing analytic continuation in the number of flavors (n_f) to reveal HTA effects.
  • Investigating N=1 super Yang-Mills theory and QCD-like SU(N) gauge theories.

Main Results:

  • Existence of hidden topological angles (HTAs) demonstrated across various quantum systems.
  • HTAs arise from saddle points and Lefschetz thimbles, distinct from theta parameters.
  • Microscopic mechanism for gluon condensate vanishing in N=1 super Yang-Mills theory identified.
  • Anomalously small condensates observed in QCD-like theories.
  • HTAs explain differences in semiclassical expansions for integer and half-integer spin particles in quantum mechanics.

Conclusions:

  • Hidden topological angles are a fundamental feature of quantum theories.
  • HTAs provide a new framework for understanding quantum phenomena, including condensates and spin-dependent expansions.
  • This work opens new avenues for research in theoretical and quantum physics.