101 research outputs found
A transition in the spectrum of the topological sector of theory at strong coupling
We investigate the strong coupling region of the topological sector of the
two-dimensional theory. Using discrete light cone quantization (DLCQ),
we extract the masses of the lowest few excitations and observe level
crossings. To understand this phenomena, we evaluate the expectation value of
the integral of the normal ordered operator and we extract the number
density of constituents in these states. A coherent state variational
calculation confirms that the number density for low-lying states above the
transition coupling is dominantly that of a kink-antikink-kink state. The
Fourier transform of the form factor of the lowest excitation is extracted
which reveals a structure close to a kink-antikink-kink profile. Thus, we
demonstrate that the structure of the lowest excitations becomes that of a
kink-antikink-kink configuration at moderately strong coupling. We extract the
critical coupling for the transition of the lowest state from that of a kink to
a kink-antikink-kink. We interpret the transition as evidence for the onset of
kink condensation which is believed to be the physical mechanism for the
symmetry restoring phase transition in two-dimensional theory.Comment: revtex4, 14 figure
The Mass Operator in the Light-Cone Representation
I argue that for the case of fermions with nonzero bare mass there is a term
in the matter density operator in the light-cone representation which has been
omitted from previous calculations. The new term provides agreement with
previous results in the equal-time representation for mass perturbation theory
in the massive Schwinger model. For the DLCQ case the physics of the new term
can be represented by an effective operator which acts in the DLCQ subspace,
but the form of the term might be hard to guess and I do not know how to
determine its coefficient from symmetry considerations.Comment: Revtex, 8 page
Light-cone quantization of two dimensional field theory in the path integral approach
A quantization condition due to the boundary conditions and the
compatification of the light cone space-time coordinate is identified at
the level of the classical equations for the right-handed fermionic field in
two dimensions. A detailed analysis of the implications of the implementation
of this quantization condition at the quantum level is presented. In the case
of the Thirring model one has selection rules on the excitations as a function
of the coupling and in the case of the Schwinger model a double integer
structure of the vacuum is derived in the light-cone frame. Two different
quantized chiral Schwinger models are found, one of them without a
-vacuum structure. A generalization of the quantization condition to
theories with several fermionic fields and to higher dimensions is presented.Comment: revtex, 14 p
Compactification in the Lightlike Limit
We study field theories in the limit that a compactified dimension becomes
lightlike. In almost all cases the amplitudes at each order of perturbation
theory diverge in the limit, due to strong interactions among the longitudinal
zero modes. The lightlike limit generally exists nonperturbatively, but is more
complicated than might have been assumed. Some implications for the matrix
theory conjecture are discussed.Comment: 13 pages, 3 epsf figures. References and brief comments added.
Nonexistent divergent graph in 0+- model delete
Nonperturbative renormalization group in a light-front three-dimensional real scalar model
The three-dimensional real scalar model, in which the symmetry
spontaneously breaks, is renormalized in a nonperturbative manner based on the
Tamm-Dancoff truncation of the Fock space. A critical line is calculated by
diagonalizing the Hamiltonian regularized with basis functions. The marginal
() coupling dependence of the critical line is weak. In the broken
phase the canonical Hamiltonian is tachyonic, so the field is shifted as
. The shifted value is determined as a function of
running mass and coupling so that the mass of the ground state vanishes.Comment: 23 pages, LaTeX, 6 Postscript figures, uses revTeX and epsbox.sty. A
slight revision of statements made, some references added, typos correcte
Quantum deformation of the Dirac bracket
The quantum deformation of the Poisson bracket is the Moyal bracket. We
construct quantum deformation of the Dirac bracket for systems which admit
global symplectic basis for constraint functions. Equivalently, it can be
considered as an extension of the Moyal bracket to second-class constraints
systems and to gauge-invariant systems which become second class when
gauge-fixing conditions are imposed.Comment: 18 pages, REVTe
Decoupling of Zero-Modes and Covariance in the Light-Front Formulation of Supersymmetric Theories
We show under suitable assumptions that zero-modes decouple from the dynamics
of non-zero modes in the light-front formulation of some supersymmetric field
theories. The implications for Lorentz invariance are discussed.Comment: 8 pages, revtex, 3 figure
Anti-Periodic Boundary Conditions in Supersymmetric DLCQ
It is of considerable importance to have a numerical method for solving
supersymmetric theories that can support a non-zero central charge. The central
charge in supersymmetric theories is in general a boundary integral and
therefore vanishes when one uses periodic boundary conditions. One is therefore
prevented from studying BPS states in the standard supersymmetric formulation
of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields
satisfy anti-periodic boundary conditions. The Hamiltonian is written as the
anti-commutator of two charges, as in SDLCQ. The anti-periodic SDLCQ we
consider breaks supersymmetry at finite resolution, but requires no
renormalization and becomes supersymmetric in the continuum limit. In
principle, this method could be used to study BPS states. However, we find its
convergence to be disappointingly slow.Comment: 9pp, 2 figure
Spontaneous symmetry breaking of (1+1)-dimensional theory in light-front field theory (III)
We investigate (1+1)-dimensional field theory in the symmetric and
broken phases using discrete light-front quantization. We calculate the
perturbative solution of the zero-mode constraint equation for both the
symmetric and broken phases and show that standard renormalization of the
theory yields finite results. We study the perturbative zero-mode contribution
to two diagrams and show that the light-front formulation gives the same result
as the equal-time formulation. In the broken phase of the theory, we obtain the
nonperturbative solutions of the constraint equation and confirm our previous
speculation that the critical coupling is logarithmically divergent. We discuss
the renormalization of this divergence but are not able to find a satisfactory
nonperturbative technique. Finally we investigate properties that are
insensitive to this divergence, calculate the critical exponent of the theory,
and find agreement with mean field theory as expected.Comment: 21 pages; OHSTPY-HEP-TH-94-014 and DOE/ER/01545-6
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