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Topological Yang–Mills Theory
In gauge theory, topological Yang–Mills theory, also known as the theta term or \theta-term is a gauge-invariant term which can be added to the action (physics), action for four-dimensional quantum field theory, field theories, first introduced by Edward Witten. It does not change the classical equations of motion, and its effects are only seen at the quantum level, having important consequences for CPT symmetry. Action Spacetime and field content The most common setting is on four-dimensional, flat spacetime (Minkowski space). As a gauge theory, the theory has a gauge symmetry under the action of a gauge group, a Lie group G, with associated Lie algebra \mathfrak through the usual Lie group-Lie algebra correspondence, correspondence. The field content is the gauge field A_\mu, also known in geometry as the principal connection, connection. It is a 1-form valued in a Lie algebra \mathfrak. Action In this setting the theta term action is S_\theta = \frac\int d^4x \, \tex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gauge Theory
In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, the Lagrangian is invariant under these transformations. The term "gauge" refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian of a physical system. The transformations between possible gauges, called gauge transformations, form a Lie group—referred to as the '' symmetry group'' or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding field (usually a vector field) called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |