Algebraic Methods in Statistical Mechanics and Quantum Field Theory

Overview


This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained ...
See more details below
Other sellers (Paperback)
  • All (16) from $1.99   
  • New (8) from $6.49   
  • Used (8) from $1.99   
Algebraic Methods in Statistical Mechanics and Quantum Field Theory

Available on NOOK devices and apps  
  • NOOK Devices
  • Samsung Galaxy Tab 4 NOOK
  • NOOK HD/HD+ Tablet
  • NOOK
  • NOOK Color
  • NOOK Tablet
  • Tablet/Phone
  • NOOK for Windows 8 Tablet
  • NOOK for iOS
  • NOOK for Android
  • NOOK Kids for iPad
  • PC/Mac
  • NOOK for Windows 8
  • NOOK for PC
  • NOOK for Mac
  • NOOK for Web

Want a NOOK? Explore Now

NOOK Book (eBook)
$10.49
BN.com price
(Save 29%)$14.95 List Price

Overview


This systematic algebraic approach concerns problems involving a large number of degrees of freedom. It extends the traditional formalism of quantum mechanics, and it eliminates conceptual and mathematical difficulties common to the development of statistical mechanics and quantum field theory. Further, the approach is linked to research in applied and pure mathematics, offering a reflection of the interplay between formulation of physical motivations and self-contained descriptions of the mathematical methods.
The four-part treatment begins with a survey of algebraic approaches to certain physical problems and the requisite tools. Succeeding chapters explore applications of the algebraic methods to representations of the CCR/CAR and quasi-local theories. Each chapter features an introduction that briefly describes specific motivations, mathematical methods, and results. Explicit proofs, chosen on the basis of their didactic value and importance in applications, appear throughout the text. An excellent text for advanced undergraduates and graduate students of mathematical physics, applied mathematics, statistical mechanics, and quantum theory of fields, this volume is also a valuable resource for theoretical chemists and biologists. 
Read More Show Less

Product Details

  • ISBN-13: 9780486472096
  • Publisher: Dover Publications
  • Publication date: 5/21/2009
  • Series: Dover Books on Physics Series
  • Pages: 352
  • Sales rank: 1,420,736
  • Product dimensions: 5.30 (w) x 8.40 (h) x 0.80 (d)

Table of Contents

GENERAL MOTIVATION
1. Why Not Stay in Fock Space?
a. Quantum Mechanics
b. Scattering Theory
c. Fock Space
d. The Relativistic, Free, Scalar-Meson Field
e. A Prototype for Quantum Field Theory: the van Hove Model
f. A Prototype for Statistical Mechanics: the BCS Model
g. Outlook
2. The Emergence of the Algebraic Approach
a. The Jordan Algebra of Observables in Traditional Quantum Mechanics
b. Structure Axioms 1 to 5 (composition laws of observables)
c. Structure Axiom 6
d. Structure Axioms 7 and 8
e. Proposition-Calculus
f. Structure Axiom 9 and GNS Construction
g. Structure Axiom 10 (uncertainty principle)
GLOBAL THEORIES
1. Basic Facts About Representations
a. Definition of a Representation
b. Irreducible Representations and Pure States
c. Examples
d. Weak Topologies and Physical Equivalence of Representations
e. von Neumann Algebras and Quasi-Equivalence of Representations
f. Traces and Types
g. S*-Algebras and Connections with Other Approaches
2. Symmetries and Symmetry Groups
a. Definition of a Symmetry
b. Symmetry Groups
c. Amendable Groups
d. Invariant and Extremal Invariant States, Asymptotic Abelianness
e. The KMS Condition
f. Decomposition Theory
CANONICAL COMMUTATION AND ANTICOMMUTATION RELATIONS
1. Canonical Commutation Relations
a. Properties of the Schrodinger Representation
b. Uniqueness Theorems
c. The C*-Algebra of the Canonical Commutation Relations
d. Haag Theorem
e. C*-Inductive Limit and IDPS
f. Representations Associated to Product States
2. Canonical Anticommutation Relations
QUASI-LOCAL THEORIES
1. General Theory of Local Systems
a. Quasi-Local Algebras and Locally Normal States
b. First Consequences of the Postulates
2. Some Simple Models of Statistical Mechanics
a. Quantum Lattice Systems
b. Free Quantum Gases
BIBLIOGRAPHY
INDEX

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)