Table of Contents
19 relations: Atiyah–Singer index theorem, Axial symmetry, Chern class, Chiral anomaly, Compact group, Connection form, Dirac operator, Eigenvalues and eigenvectors, Feynman slash notation, Field strength, Functional determinant, Hermann Grassmann, Jacobian matrix and determinant, Lie algebra, Orthonormality, Partition function (quantum field theory), Physics, Quantum field theory, Representation of a Lie group.
- Anomalies (physics)
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related to the dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data).
See Fujikawa method and Atiyah–Singer index theorem
Axial symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.
See Fujikawa method and Axial symmetry
Chern class
In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles.
See Fujikawa method and Chern class
Chiral anomaly
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. Fujikawa method and chiral anomaly are Anomalies (physics).
See Fujikawa method and Chiral anomaly
Compact group
In mathematics, a compact (topological) group is a topological group whose topology realizes it as a compact topological space (when an element of the group is operated on, the result is also within the group).
See Fujikawa method and Compact group
Connection form
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms.
See Fujikawa method and Connection form
Dirac operator
In mathematics and quantum mechanics, a Dirac operator is a differential operator that is a formal square root, or half-iterate, of a second-order operator such as a Laplacian.
See Fujikawa method and Dirac operator
Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector is a vector that has its direction unchanged by a given linear transformation.
See Fujikawa method and Eigenvalues and eigenvectors
Feynman slash notation
In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation).
See Fujikawa method and Feynman slash notation
Field strength
In physics, field strength is the magnitude of a vector-valued field (e.g., in volts per meter, V/m, for an electric field E).
See Fujikawa method and Field strength
Functional determinant
In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself.
See Fujikawa method and Functional determinant
Hermann Grassmann
Hermann Günther Grassmann (Graßmann,; 15 April 1809 – 26 September 1877) was a German polymath known in his day as a linguist and now also as a mathematician.
See Fujikawa method and Hermann Grassmann
Jacobian matrix and determinant
In vector calculus, the Jacobian matrix of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
See Fujikawa method and Jacobian matrix and determinant
Lie algebra
In mathematics, a Lie algebra (pronounced) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity.
See Fujikawa method and Lie algebra
Orthonormality
In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal unit vectors.
See Fujikawa method and Orthonormality
Partition function (quantum field theory)
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism.
See Fujikawa method and Partition function (quantum field theory)
Physics
Physics is the natural science of matter, involving the study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force.
See Fujikawa method and Physics
Quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics.
See Fujikawa method and Quantum field theory
Representation of a Lie group
In mathematics and theoretical physics, a representation of a Lie group is a linear action of a Lie group on a vector space.
See Fujikawa method and Representation of a Lie group
See also
Anomalies (physics)
- Anomaly (physics)
- Anomaly matching condition
- Central charge
- Chiral anomaly
- Conformal anomaly
- Fujikawa method
- Gauge anomaly
- Global anomaly
- Gravitational anomaly
- Green–Schwarz mechanism
- Instanton
- Konishi anomaly
- Large gauge transformation
- Mixed anomaly
- Parity anomaly
- Peccei–Quinn theory
- RST model
- Sphaleron
References
Also known as Fujikawa's method.