The Requirements of a Basic Physical Theory

Basil S. Davis

Mingsheng Ying, Yuan Feng

This chapter is intended to introduce some basic notions of quantum theory needed in the subsequent chapters for the reader who is not familiar with them. Quantum mechanics is a fundamental physics subject that studies the phenomena at the atomic and subatomic scales. This chapter introduces the required mathematical tools and presents the postulates mainly through their mathematical formalisms. The physics interpretation of these is only very briefly discussed.

Eugene Paul Wigner

Marc Illa, Martin J. Savage A

We explore the potential of D-Wave's quantum annealers for computing some of the basic components required for quantum simulations of standard model physics. By implementing a basic multigrid (including ``zooming'') and specializing Feynman-clock algorithms, D-Wave's Advantage is used to study harmonic and anharmonic oscillators relevant for lattice scalar field theories and effective field theories, the time evolution of a single plaquette of SU(3) Yang-Mills lattice gauge field theory, and the dynamics of flavor entanglement in four-neutrino systems.

Abdelkader Intissar

In this work, we present a complete spectral study of a family of non-normal operators arising in Reggeon field theory. This family of operators is an original example who permit us to discover the recent theory of physical requirement of space-time reflection symmetry (PT symmetry) without losing any of the essential physical features of quantum mechanics [Bender]. Early studies of Reggeon field theory, in the late 1970s led a number of investigators to observe that model cubic quantum-mechanical Hamiltonians might have real eigenvalues [Bower et al]. The study of this family of operators, permit us to discover some fine results of Spectral Theory and Functional Analysis in particular the results connected with completeness of elementary solutions of mathematical physics problems. We use knowledge basics of holomorphic functions of one complex variable and the properties of Hilbert spaces. In this work the knowledge of spectral theory and the functional analysis of standard level is required (see [Kato], [Ghohberg2 et al] and [Markus]). It is also requested to know the basic properties of semigroup theory see for example ([Pazy]).