77 research outputs found
Proof of Serban's conjecture
We prove Serban's conjecture which simplifies greatly the expression of the
advanced single-particle Green function in the Calogero-Sutherland model. The
importance of proving this conjecture is that it reorganizes the form factor in
terms of two dimensional Coulomb gaz correlators and confirms the possible
existence of a bosonization procedure for this system.Comment: LaTex, 29
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https://digitalcommons.library.umaine.edu/mmb-vp/4855/thumbnail.jp
Exact renormalization group equations and the field theoretical approach to critical phenomena
After a brief presentation of the exact renormalization group equation, we
illustrate how the field theoretical (perturbative) approach to critical
phenomena takes place in the more general Wilson (nonperturbative) approach.
Notions such as the continuum limit and the renormalizability and the presence
of singularities in the perturbative series are discussed.Comment: 15 pages, 7 figures, to appear in the Proceedings of the 2nd
Conference on the Exact Renormalization Group, Rome 200
Random matrix analysis of the QCD sign problem for general topology
Motivated by the important role played by the phase of the fermion
determinant in the investigation of the sign problem in lattice QCD at nonzero
baryon density, we derive an analytical formula for the average phase factor of
the fermion determinant for general topology in the microscopic limit of chiral
random matrix theory at nonzero chemical potential, for both the quenched and
the unquenched case. The formula is a nontrivial extension of the expression
for zero topology derived earlier by Splittorff and Verbaarschot. Our
analytical predictions are verified by detailed numerical random matrix
simulations of the quenched theory.Comment: 33 pages, 9 figures; v2: minor corrections, references added, figures
with increased statistics, as published in JHE
Parametric Representation of Noncommutative Field Theory
In this paper we investigate the Schwinger parametric representation for the
Feynman amplitudes of the recently discovered renormalizable quantum
field theory on the Moyal non commutative space. This
representation involves new {\it hyperbolic} polynomials which are the
non-commutative analogs of the usual "Kirchoff" or "Symanzik" polynomials of
commutative field theory, but contain richer topological information.Comment: 31 pages,10 figure
The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach
We consider the gap probability for the Pearcey and Airy processes; we set up
a Riemann--Hilbert approach (different from the standard one) whereby the
asymptotic analysis for large gap/large time of the Pearcey process is shown to
factorize into two independent Airy processes using the Deift-Zhou steepest
descent analysis. Additionally we relate the theory of Fredholm determinants of
integrable kernels and the theory of isomonodromic tau function. Using the
Riemann-Hilbert problem mentioned above we construct a suitable Lax pair
formalism for the Pearcey gap probability and re-derive the two nonlinear PDEs
recently found and additionally find a third one not reducible to those.Comment: 43 pages, 7 figures. Final version with minor changes. Accepted for
publication on International Mathematical Research Notice
Mixed correlation functions in the 2-matrix model, and the Bethe ansatz
Using loop equation technics, we compute all mixed traces correlation
functions of the 2-matrix model to large N leading order. The solution turns
out to be a sort of Bethe Ansatz, i.e. all correlation functions can be
decomposed on products of 2-point functions. We also find that, when the
correlation functions are written collectively as a matrix, the loop equations
are equivalent to commutation relations.Comment: 38 pages, LaTex, 24 figures. misprints corrected, references added, a
technical part moved to appendi
Once again on the equivalence theorem
We present the proof of the equivalence theorem in quantum field theory which
is based on a formulation of this problem in the field-antifield formalism. As
an example, we consider a model in which a different choices of natural finite
counterterms is possible, leading to physically non-equivalent quantum theories
while the equivalent theorem remains valid.Comment: 12 pages, LATEX, report number was correcte
The Regge Limit for Green Functions in Conformal Field Theory
We define a Regge limit for off-shell Green functions in quantum field
theory, and study it in the particular case of conformal field theories (CFT).
Our limit differs from that defined in arXiv:0801.3002, the latter being only a
particular corner of the Regge regime. By studying the limit for free CFTs, we
are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak
coupling. The dominance of Feynman graphs where only two high momentum lines
are exchanged in the t-channel, follows simply from the free field analysis. We
can then define the BFKL kernel in terms of the two point function of a simple
light-like bilocal operator. We also include a brief discussion of the gravity
dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit
defined here and previous work in CFT. Clarification of causal orderings in
the limit. References adde
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