What is Gauge fixing: Definition and 19 Discussions

In the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.
Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.

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  1. T

    A Understanding Ghost Fields in QED: Eliminating Unphysical Degrees of Freedom"

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  2. G

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  3. tomdodd4598

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  4. L

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  5. Michael Price

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  6. V

    Gauge invariance in GR perturbation theory

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  7. Urs Schreiber

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  8. carllacan

    I How does Gauge fixing fix anything?

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  9. D

    Gauge fixing and gauge transformations

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  10. T

    Why does gauge fixing break gauge symmetry?

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  11. T

    Gauge Fixing Term and Equations of Motion

    Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...
  12. michael879

    Gauge Fixing in Yang-Mills gauge theory

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  13. N

    Why are there several gauge fixing choice for gauge symmetry fields?

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  14. K

    What does it mean by independent (in gauge fixing of EM field)

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  15. tom.stoer

    Gribov (gauge fixing) ambiguities in quantum gravity

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  16. N

    Gauge Fixing Term: Physical Effects & Role in Spin Components

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  17. I

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  18. K

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  19. S

    Gauge fixing and residual symmetries

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