37,913 research outputs found
T-systems, Y-systems, and cluster algebras: Tamely laced case
The T-systems and Y-systems are classes of algebraic relations originally
associated with quantum affine algebras and Yangians. Recently they were
generalized to quantum affinizations of quantum Kac-Moody algebras associated
with a wide class of generalized Cartan matrices which we say tamely laced.
Furthermore, in the simply laced case, and also in the nonsimply laced case of
finite type, they were identified with relations arising from cluster algebras.
In this note we generalize such an identification to any tamely laced Cartan
matrices, especially to the nonsimply laced ones of nonfinite type.Comment: 31 pages, final version to appear in the festschrift volume for
Tetsuji Miwa, "Infinite Analysis 09: New Trends in Quantum Integrable
Systems
Structure of seeds in generalized cluster algebras
We study generalized cluster algebras introduced by Chekhov and Shapiro. When
the coefficients satisfy the normalization and quasi-reciprocity conditions,
one can naturally extend the structure theory of seeds in the ordinary cluster
algebras by Fomin and Zelevinsky to generalized cluster algebras. As the main
result, we obtain formulas expressing cluster variables and coefficients in
terms of c-vectors, g-vectors, and F-polynomials.Comment: 15 pages; v2:minor revision; v3:typos corrected, to appear in Pacific
J. Mat
Wightman-Function Approach to the Relativistic Complex-Ghost Field Theory
The relativistic complex-ghost field theory is covariantly formulated in
terms of Wightman functions. The Fourier transform of the 2-point Wightman
function of a complex-ghost pair is explicitly calculated, and its spontaneous
breakdown of Lorentz invariance is compared with that of the corresponding
Feynman integral.Comment: 10 page
Unobservable Higgs Boson and Spontaneous Violation of Lorentz Invariance
The standard theory of elementary particle physics is modified in such a way
that the Higgs boson becomes unobservable and Lorentz invariance is slightly
violated at the level of the S-matrix. The basic technique of realizing these
properties without violating the unitarity of the physical S-matrix is the use
of the complex-ghost quantum field theory.Comment: 8 page
- …