相关论文: An Introduction to the Quantum Supermembrane

The stable envelopes of Okounkov et al. realize some representations of quantum algebras associated to quivers, using geometry. We relate these geometric considerations to quantum field theory. The main ingredients are the supersymmetric…

The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of…

Recently Sekino and Yoneya proposed a way to regularize the world volume theory of membranes wrapped around $S^1$ by matrices and showed that one obtains matrix string theory as a regularization of such a theory. We show that this…

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…

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.

We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the…

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…

At the macrosopic level we study candidate 3D effective field theories associated to M theory in three dimensions. These represent analogs of 11D supergravity for eleven dimensional M-theory. At the microscopic level we study various world…

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…

Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".

We discuss the superconformal quantum mechanics arising from the M2-branes. We begin with a comprehensive review on the superconformal quantum mechanics and emphasize that conformal symmetry and supersymmetry in quantum mechanics contain a…

In this paper, we derive a soft theorem at leading and subleading orders within the context of BFSS matrix theory. Specifically, we consider the effective field theory describing interactions between bound states of D0-branes at leading…

We propose a new non-perturbative method for studying UV complete unitary quantum field theories (QFTs) with a mass gap in general number of spacetime dimensions. The method relies on unitarity formulated as positive semi-definiteness of…

In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy…

We provide a one-to-one correspondence between line operators and states in four-dimensional CFTs with continuous 1-form symmetries. In analogy with 0-form symmetries in two dimensions, such CFTs have a free photon realisation and enjoy an…

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection…

A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…