Basis of symmetric polynomials for many-boson light-front wave functions

Nambu - Goldstone Boson on the Light - Front ∗

Spontaneous breakdown of the continuous symmetry is studied in the framework of discretized light-front quantization. We consider linear sigma model in 3+1 dimension and show that the careful treatment of zero modes together with the regularization of the theory by introducing NG boson mass leads to the correct description of Nambu-Goldstone phase on the light-front. Recently the light-front (L...

Chiral Boson Theory on the Light - Front

The front form framework for describing the quantized theory of chiral boson is discussed. It avoids the conflict with the requirement of the principle of microcausality as is found in the conventional instant form treatment. The discussion of the Floreanini-Jackiw model and its modified version for describing the chiral boson becomes very transparent on the light-front.

Introductions to Symmetric Polynomials and Symmetric Functions

Symmetric polynomials and symmetric functions are ubiquitous in mathematics and mathematical physics. For example, they appear in elementary algebra (e.g. Viete’s Theorem), representation theories of symmetric groups and general linear groups over C or finite fields. They are also important objects to study in algebraic combinatorics. Via their close relations with representation theory, the th...

Symmetric Functions and Macdonald Polynomials

The ring of symmetric functions Λ, with natural basis given by the Schur functions, arise in many different areas of mathematics. For example, as the cohomology ring of the grassmanian, and as the representation ring of the symmetric group. One may define a coproduct on Λ by the plethystic addition on alphabets. In this way the ring of symmetric functions becomes a Hopf algebra. The Littlewood–...

Symmetric Functions and Hall Polynomials