Algebraic quantum field theory: objectives, methods, and results

• URL: http://arxiv.org/abs/2305.12923v2
• Date: Mon, 22 Jul 2024 11:27:35 GMT
• Title: Algebraic quantum field theory: objectives, methods, and results
• Authors: Detlev Buchholz, Klaus Fredenhagen,
• Abstract summary: Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics. In its framework the entire state space of a theory is covered, starting from the vacuum over arbitrary configurations of particles to thermal equilibrium and non-equilibrium states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Algebraic quantum field theory is a general mathematical framework for relativistic quantum physics, based on the theory of operator algebras. It comprises all observable and operational aspects of a theory. In its framework the entire state space of a theory is covered, starting from the vacuum over arbitrary configurations of particles to thermal equilibrium and non-equilibrium states. It provides a solid foundation for structural analysis, the physical interpretation of the theory and the development of new constructive schemes. This survey is commissioned by the Encyclopedia of Mathematical Physics, edited by M. Bojowald and R.J. Szabo. It is to be published by the Elsevier publishing house.

Related papers

• Entanglement in Lifshitz Fermion Theories [0.0]
  We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above.
  arXiv  Detail & Related papers  (2024-05-28T12:02:47Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• Entanglement Witnessing for Lattice Gauge Theories [0.0]
  Entanglement is assuming a central role in modern quantum many-body physics. We develop the theoretical framework of entanglement witnessing for lattice gauge theories. We illustrate the concept at the example of a $mathrmU(1)$ lattice gauge theory in 2+1 dimensions.
  arXiv  Detail & Related papers  (2022-07-01T18:01:21Z)
• Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory [0.0]
  We suggest bundle theoretic descriptions of massive single-particle state spaces, which are basic building blocks of Relativistic Quantum Information Theory. A link between the usual Hilbert space description is provided by a generalized induced representation construction on the $L2$-section space of the bundle. Some of the theoretical implications of the formalism will be explored at the end of the paper.
  arXiv  Detail & Related papers  (2022-01-12T06:07:19Z)
• Quantum Simulation of Conformal Field Theory [77.34726150561087]
  We describe a quantum algorithm to simulate the dynamics of conformal field theories. A full analysis of the approximation errors suggests near-term applicability.
  arXiv  Detail & Related papers  (2021-09-29T06:44:33Z)
• Geometric and algebraic approaches to quantum theory [0.0]
  We show how to formulate physical theory taking as a starting point the set of states. The equations of motion and the formulas for probabilities of physical quantities are analyzed.
  arXiv  Detail & Related papers  (2021-02-18T06:39:01Z)
• From Boolean Valued Analysis to Quantum Set Theory: Mathematical Worldview of Gaisi Takeuti [0.0]
  Gaisi Takeuti introduced Boolean valued analysis around 1974 to provide systematic applications of Boolean valued models of set theory to analysis. He then stepped forward to construct set theory based on quantum logic, as the first step to construct "quantum mathematics" We analyze Takeuti's mathematical world view underlying his program from two perspectives.
  arXiv  Detail & Related papers  (2021-02-07T17:17:06Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
  We review a number of issues in foundations of quantum theory and quantum cosmology. These issues can be considered as a part of the scientific legacy of H.D. Zeh.
  arXiv  Detail & Related papers  (2020-06-28T18:07:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.