23 research outputs found
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