Dirac equation for membranes

Dirac's idea of taking the square root of constraints is applied to the case of extended objects concentrating on membranes in D=4 space-time dimensions. The resulting equation is Lorentz invariant and predicts an infinite hierarchy of positive and negative masses (tension). There are no tachyonic solutions.Comment: 5 pages, 1 figure, v2: improved version, accepted for publication as a Brief Report in Physical Review

The hamiltonian study of supersymmetric Yang-Mills quantum mechanics

The hamiltonian formulation of Supersymmetric Yang-Mills quantum mechanics (SYMQM) is discussed. We focus on the Fock space formulation of the models since it is convenient for the numerical analysis, however some novel analytical results are also pointed out.Comment: 3 page

Quantum systems in a cut Fock space

Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite dimensional Hilbert space is studied in detail. The difference between systems with discrete and continuous energy spectra is emphasized. In particular a new scaling law, characteristic for nonlocalized, states is found. Some applications for supersymmetric quantum mechanics are briefly outlined.Comment: 10 page

Classical trajectories and quantum supersymmetry

We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical counterpart of this system. A similar analysis is then done for an alike, but non-supersymmetric system. The comparison of theses classical and quantum results may serve as a suggestion about classical manifestations of supersymmetry.Comment: 16 pages, 12 figures, 5 tables, some misspellings correcte

Supersymmetric Yang-Mills quantum mechanics in various dimensions

Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting continuous and discrete spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO(9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.Comment: Talk presented at the Eighth Workshop on Non-Perturbative QCD, Paris, June 2004; 8 pages, 4 figure

On gauge transformation property of coordinate independent SO(9) vector states in SU(2) Matrix Theory

We investigate coordinate independent SO(9) vector states in SU(2) Matrix theory. There are 36 vector states, and we determine what representations of SU(2) they are decomposed into. Among them we find a unique set of states transforming in adjoint representation. We show that this set of states can appear as the linear term in the coordinate matrices in Taylor expansion of zero energy bound state wavefunction around the origin i.e. it satisfies the condition of full supersymmetry.Comment: 21 pages, no figure, v2: minor correction v3: signs in (3.46) and (3.51) corrected, further calculation on the linear term of the expansion of the wavefunction added, and the conclusion about it changed, v3: minor change in the references, version published in JHE

Supergravitons from one loop perturbative N=4 SYM

We determine the partition function of 1/16 BPS operators in N=4 SYM at weak coupling at the one-loop level in the planar limit. This partition function is significantly different from the one computed at zero coupling. We find that it coincides precisely with the partition function of a gas of 1/16 BPS `supergravitons' in AdS_5xS^5.Comment: 22 pages; v2: references adde

Analytic calculation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics

We propose a method for the evaluation of Witten index in D=2 supersymmetric Yang-Mills quantum mechanics. We rederive a known result for the SU(2) gauge group and generalize it to any SU(N) gauge group.Comment: 21 pages, 5 figure

A note on the principle of least action and Dirac matrices

Many Lagrangians of physical theories can be expressed as eigenvalues of certain, relatively simple, matrices involving Dirac gamma matrices. We give concrete examples for Lagrangian corresponding to a point particle coupled to electromagnetic field, electrodynamics, nonabelian gauge theories, extended objects and gravity. We also discuss (in case of a point particle) what are the implications of the least action principle applied to matrix Lagrangians