Notes on Fock Space

نویسنده

  • PETER TINGLEY
چکیده

These notes are intended as a fairly self contained explanation of Fock space and various algebras that act on it, including a Clifford algebras, a Weyl algebra, and an affine Kac-Moody algebra. We also discuss how the various algebras are related, and in particular describe the celebrated boson-fermion correspondence. We finish by briefly discussing a deformation of Fock space, which is a representation for the quantized universal enveloping algebra Uq(ŝl`).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Notes on fermionic Fock space for number theorists

version of my " notebook ". It is a compilation of exercises, worked examples and key references (along with provocative remarks) that I have compiled in order to help myself and (fingers crossed) others learn their way around fermionic Fock space. Eventually (again, fingers crossed) the notebook will become a monograph suitable for use by, say, second year graduate students with an interest in...

متن کامل

Notes on Quantum Teichmüller Theory

We review the Fock-Goncharov formalism for quantum Teichmüller theory. By a conjecture of H. Verlinde, the Hilbert space of quantum Teichmüller theory can be viewed as the space of conformal blocks for the two-dimensional Liouville conformal field theory. The Teichmüller space of a surface also arises in the quantization of SL2(R)-Chern-Simons theory. We review these relationships and indicate ...

متن کامل

Quantum filtering: a reference probability approach

These notes are intended as an introduction to noncommutative (quantum) filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as the least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. Next we describe the HudsonParthasarathy quantum Itô calculus and it...

متن کامل

Notes on Free Probability Theory

Lecture 1. Free Independence and Free Harmonic Analysis. 2 1.1. Probability spaces. 2 1.2. Non-commutative probability spaces. 3 1.3. Classical independence. 4 1.4. Free products of non-commutative probability spaces. 5 1.5. Free Fock space. 6 1.6. Free Central Limit Theorem. 8 1.7. Free Harmonic Analysis. 10 1.8. Further topics. 16 Lecture 2. Random Matrices and Free Probability. 17 2.1. Rando...

متن کامل

Fock Space Realizations of Imaginary Verma Modules

The motivation for this paper goes back to at least the work of A. Borel, R. Bott and A. Weil on their geometric construction of irreducible representations of complex simple Lie groups, and the related work of B. Kostant [10] and J. Bernšteı̆n, I. Gel′fand and S. Gel′fand [2]. Articles more closely related to ours are those of H. Jakobsen and V. Kac [9] and then presumably Wakimoto [11] and mor...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011