Gauging what's real : the conceptual foundations of contemporary gauge theories / Richard Healey.

Format:

Book

Author/Creator:

Healey, Richard.

Language:

English

Subjects (All):

Gauge fields (Physics).

Physics--Philosophy.

Physics.

Physical Description:

xix, 297 pages : illustrations ; 24 cm

Place of Publication:

Oxford ; New York : Oxford University Press, 2007.

Summary:

Gauge theories have provided our most successful representations of the fundamental forces of nature. How, though, do such representations work? Interpretations of gauge theory aim to answer this question. Through understanding how a gauge theory's representations work, we are able to say what kind of world our gauge theories reveal to us. A gauge theory's representations are mathematical structures. These may be transformed among themselves while certain features remain the same. Do the representations related by such a gauge transformation merely offer alternative ways of representing the very same situation? If so, then gauge symmetry is a purely formal property since it reflects no corresponding symmetry in nature.

Gauging What's Real describes the representations provided by gauge theories in both classical and quantum physics. Richard Healey defends the thesis that gauge transformations are purely formal symmetries of almost all the classes of representations provided by each of our theories of fundamental forces. He argues that evidence for classical gauge theories of forces (other than gravity) gives us reason to believe that loops rather than points are the locations of fundamental properties. In addition to exploring the prospects of extending this conclusion to the quantum gauge theories of the Standard Model of elementary particle physics, Healey assesses the difficulties faced by attempts to base such ontological conclusions on the success of these theories.

Contents:

What is a gauge theory?

Classical electromagnetism : a paradigm gauge theory

A fiber bundle formulation

Electromagnetic interactions of quantum particles

Electromagnetic interactions of matter fields

The Aharonov-Bohm effect

Fiber bundles

A gauge-invariant, local explanation?

Geometry and topology in the Aharonov-Bohm effect

Locality in the Aharonov-Bohm effect

Lessons for classical electromagnetism

Classical gauge theories

Non-Abelian Yang-Mills theories

The fiber bundle formulation

Loops, groups, and hoops

Topological issues

A fiber bundle formulation of general relativity

A gravitational analog to the Aharonov-Bohm effect

Interpreting classical gauge theories

The no gauge potential properties view

The localized gauge potential properties view

Problems defining theoretical terms

Leeds's view

Maudlin's interpretation

The non-localized gauge potential properties view

A holonomy interpretation

Epistemological considerations

Objections considered

Semantic considerations

Metaphysical implications : non-separability and holism

Quantized Yang-Mills gauge theories

How to quantize a classical field

Coulomb gauge quantization

Lorenz gauge quantization

Classical electromagnetism as a constrained Hamiltonian system

The free Maxwell field as a Hamiltonian system

Path-integral quantization

Canonical quantization of non-Abelian fields

Path-integral quantization of non-Abelian fields

Interacting fields in the Lagrangian formulation

The empirical import of gauge symmetry

Two kinds of symmetry

Observing gauge symmetry?

The gauge argument

Ghost fields

Spontaneous symmetry-breaking

The [theta]-vacuum

Anomalies

Loop representations

The significance of loop representations

Loop representations of the free Maxwell field

Loop representations of other free Yang-Mills fields

Interacting fields in loop representations

The [theta]-vacuum in a loop representation

Interpreting quantized Yang-Mills gauge theories

Auyang's event ontology

Problems of interpreting a quantum field theory

Particle interpretations

Bohmian interpretations

Copenhagen interpretations

Everettian interpretations

Modal interpretations

Conclusions

Electromagnetism and its generalizations

The constrained Hamiltonian formalism

Alternative quantum representations

Algebraic quantum field theory

Interpretations of quantum mechanics

The Copenhagen interpretation

Bohmian mechanics

Modal interpretations.

Notes:

Includes bibliographical references (pages [280]-286) and index.

ISBN:

0199287961

9780199287963

OCLC:

137312963