Related papers: Symmetry as a source of hidden coherent structures…
It is an interesting and open problem to trace the origin of the pseudospin symmetry in nuclear single-particle spectra and its symmetry breaking mechanism in actual nuclei. In this report, we mainly focus on our recent progress on this…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
We consider some simple examples of supersymmetric quantum mechanical systems and explore their possible geometric interpretation with the help of geometric aspects of real Clifford algebras. This leads to natural extensions of the…
In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
It is quite common to use the generalized probabilistic theories (GPTs) as generic models to reconstruct quantum theory from a few basic principles and to gain a better understanding of the probabilistic or information theoretic foundations…
We study conformally invariant boundary conditions that break part of the bulk symmetries. A general theory is developped for those boundary conditions for which the preserved subalgebra is the fixed algebra under an abelian orbifold group.…
Complex numbers enter fundamental physics in at least two rather distinct ways. They are needed in quantum theories to make linear differential operators into Hermitian observables. Complex structures appear also, through Hodge duality, in…
We introduce the notion of a generalized partial dynamical symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6)…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
The purpose of this work is to establish the spectral setting of some generalized Laplace operators associated to a generic $G$-invariant metric on a compact homogeneous space $M=G/K$. We show that this generic spectral configuration…
We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in…
We use strong complementarity to introduce dynamics and symmetries within the framework of CQM, which we also extend to infinite-dimensional separable Hilbert spaces: these were long-missing features, which open the way to a wealth of new…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
The symmetries described by Pin groups are the result of combining a finite number of discrete reflections in (hyper)planes. The current work shows how an analysis using geometric algebra provides a picture complementary to that of the…
Group theory (GT) provides a rigorous framework for studying symmetries in various disciplines in physics ranging from quantum field theories and the standard model to fluid mechanics and chaos theory. To date, the application of such a…
We review known and we present new results on three types of short distance structures of observables which typically appear in studies of quantum group related algebras. In particular, one of the short distance structures is shown to…
We make some general remarks on long-ranged configurations in gauge or diffeomorphism invariant theories where the fields are allowed to assume some non vanishing values at spatial infinity. In this case the Gauss constraint only eliminates…
Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are…
Two examples, not connected at present, from author's papers (Nuovo Cim., 1992, v.105A, p.77 [hep-th/0207210] and GRG, 1999, v.31, p.1431 [gr-qc/0207017]) are considered here in which a physical model has discrete symmetries and additional…