In theoretical physics, a Fierz identity is an identity that allows one to rewrite bilinears of the product of two spinors as a linear combination of...

Markus Eduard Fierz (20 June 1912 – 20 June 2006) was a Swiss physicist, particularly remembered for his formulation of spin–statistics theorem, and for...

Pauli matrices Gell-Mann matrices Higher-dimensional gamma matrices Fierz identity Spacetime algebra Kukin 2016. Lonigro 2023. Jost 2002. Tong 2007, These...

trace-orthogonal set spanning all 3×3 matrices, it is straightforward to find two Fierz completeness relations, (Li & Cheng, 4.134), analogous to that satisfied...

Clifford module Complex spin structure Dirac operator Exterior algebra Fierz identity Gamma matrices Generalized Clifford algebra Geometric algebra Higher-dimensional...

spacetime algebra. physics portal Higher-dimensional gamma matrices Fierz identity Weinberg 2005, Equation 5.4.6 Weinberg 2005, Equation 5.4.4 Section...

becomes unwieldy when complicated properties of the spinors, such as Fierz identities, are needed. The language of Clifford algebras (sometimes called geometric...

the gamma matrices. These five quantities are inter-related by the Fierz identities. Their values are used in the Lounesto spinor field classification...

winding history, dating back to the 1930s when Wolfgang Pauli and Markus Fierz first developed a theory of a massive spin-2 field propagating on a flat...

emission probes Field equation Field of Streams Field rate Field strength Fierz identity Fifth force Figure-8 laser Figure of the Earth Figuring Filament propagation...

and Petiau (around 1938–1939) see Duffin–Kemmer–Petiau algebra. The Dirac–Fierz–Pauli formalism was more sophisticated than Majorana's, as spinors were...

{1}{4}}\partial ^{\mu }h\partial _{\mu }h,} where this Lagrangian is known as the Fierz–Pauli Lagrangian. For a massless spin-2 field, this kinetic term can be...

that fail this test. The classic example is the spin-two field theory of Fierz and Pauli; the field equations imply that gravitating bodies move in straight...

{\delta \Gamma [\phi ]}{\delta \phi (x)}}.} This identity is an example of a Slavnov–Taylor identity. It is identical to the requirement that the effective...

\ D_{\mu }=I\ \partial _{\mu }-i\ g\ T^{a}\ A_{\mu }^{a}\ ,} I is the identity matrix (matching the size of the generators),   A μ a   {\displaystyle...

{\displaystyle \psi _{\alpha }} be a single-particle state, let 1 be the tensor identity (it is the generator of the zero-particle space C and satisfies ψ α ≡ 1...

of higher spin (compare Dirac matrices), elaborated upon by Fierz (1939), see also Fierz & Pauli (1939), and proposed precursors of the Bargmann-Wigner...

theories allows simplification of some computations: for example Ward identities connect different renormalization constants. The first gauge theory quantized...

the transformation is made, then B remains unchanged, since (with the identity ∇ × ∇ ψ = 0 {\displaystyle \nabla \times \nabla \psi =0} ) B = ∇ × ( A...

notable early work, Rarita and Schwinger formulated the abstract Pauli and Fierz theory of the spin-3/2 field in a concrete form, as a vector of Dirac spinors...

integral. Indeed, for any square matrix M {\displaystyle M} , one has the identity ∫ exp ⁡ [ − θ T M η ] d θ d η = det M {\displaystyle \int \exp \left[-\theta...

authors choose different signs. The partial derivative term includes a 3 × 3 identity matrix, conventionally not written for simplicity. The quark fields in...

Higher-dimensional gamma matrices Nonlinear Schrödinger equation Pokhozhaev's identity for the stationary nonlinear Dirac equation Soler model Thirring model...

 L)ψ. If we restrict attention to elements of the group connected to the identity, then the anti-unitary case does not occur. Let (a, L) and (b, M) be two...

}\right)_{B}=Z_{3}\,F_{\mu \nu }F^{\mu \nu }.} Gauge invariance, via a Ward–Takahashi identity, turns out to imply that we can renormalize the two terms of the covariant...

and later (1936) extended it to particles of any half-integer spin before Fierz and Pauli subsequently found the same equations in 1939, and about a decade...

equal to 1. In physics, such a quantity is "equal to 1 as an operator identity". In mathematics, it "weakly converges to 1". In either case, it is 1 in...

particular, there are two connected components. One contains the identity and is called the identity component, the other is called the disconnected component...

\phi (x)\phi (y)\right\rangle =0} Where the derivatives act on x, and the identity is true everywhere except when x and y coincide, and the operator order...

Symmetry in quantum mechanics Topological quantum field theory Ward–Takahashi identity Wheeler–Feynman absorber theory Wigner's classification Wigner's theorem...