168 research outputs found
Chiral Symmetry {\it Breaking} in the Light-Cone Representation ()
In this paper I shall discuss the way in which vacuum structure and
condensates occur in the light-cone representation. I shall particularly
emphasize the mechanism by which the mass squared of a composite such as the
pion comes to depend linearly on the bare mass of its Fermion constituents. I
shall give details in two dimensions then discuss the case of four dimensions
more speculatively.Comment: 10 pages and uses elsar
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
Induced Operators in QCD
Light-cone quantization always involves the solution of differential
constraint equations. The solutions to these equations include integration
constants (fields independent of ). These fields are unphysical but when
they are consistently removed from the dynamics, additional operators (induced
operators), which would not be present if the integration constants were simply
set to zero, are included in the dynamics. These induced operators can be taken
to act in the usual light-cone subspace, for instance, the space used for DLCQ.
Here, I shall give a derivation of two such operators. The operators are
derived starting from the QCD Lagrangian but the derivation involves some
guesses. The operators will provide for the linear growth of the pion mass
squared with the quark bare mass and for the splitting of the pi and the rho at
zero quark mass.Comment: 8 pages. Talk presented at Light-Cone 2004 at the VU Amsterda
Some Lessons from the Schwinger Model
I shall recall a number of solutions to the Schwinger model in different
gauges, having different boundary conditions and using different quantization
surfaces. I shall discuss various properties of these solutions emphasizing the
degrees of freedom necessary to represent the solution, the way the operator
products are defined and the effects these features have on the chiral
condensate.Comment: 10 pages, uses RevTe
Resolving the Ambiguity in a Homogeneous Electric Background
I present an exact solution for the Heisenberg picture, Dirac electron in the
presence of an electric field which depends arbitrarily upon the light cone
time parameter . This is the largest class of background
fields for which the mode functions have ever been obtained. The solution
applies to electrons of any mass and in any spacetime dimension. The
traditional ambiguity at is explicitly resolved. It turns out that
the initial value operators include not only at
but also at . Pair creation
is a discrete and instantaneous event on the light cone, so one can compute the
particle production rate in real time. In dimensions one can also see
the anomaly. Another novel feature of the solution is that the expectation
value of the current operators depends nonanalytically upon the background
field. This seems to suggest a new, strong phase of QED.Comment: 5 pages, LaTeX 2 epsilon, 2 figures, talk presented at the
International Workshop on Light-cone Physics, Particles and Strings, Trento,
Italy, Sept. 3-11, 200
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