Renormalization group On-shell scheme Minimal subtraction scheme
Regularization
Dimensional regularization Pauli–Villars regularization Lattice regularization Zeta function regularization Causal perturbation theory Hadamard regularization Point-splitting regularization
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In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators. The technique is now commonly applied to problems in physics, but has its origins in attempts to give precise meanings to ill-conditioned sums appearing in number theory.
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In mathematics and theoretical physics, zetafunctionregularization is a type of regularization or summability method that assigns finite values to divergent...
dimensional regularization can be used to study the physics of crystals that macroscopically appear to be fractals. It has been argued that Zetafunction regularization...
The Riemann zetafunction or Euler–Riemann zetafunction, denoted by the Greek letter ζ (zeta), is a mathematical function of a complex variable defined...
inspiration for later attempts at regularization and renormalization in quantum field theory. (See also regularization (physics) for an alternative way...
then its value at s = −1 is called the zetaregularized sum of the series a1 + a2 + ... Zetafunctionregularization is nonlinear. In applications, the numbers...
x^{m-2r}=-{\frac {a^{m-2r+1}}{m-2r+1}}.} Note that this involves (see zetafunctionregularization) I ( n , Λ ) = ∫ 0 Λ d x x n {\displaystyle I(n,\Lambda )=\int...
Riemann zetafunction is a function in complex analysis, which is also important in number theory. It is often denoted ζ ( s ) {\displaystyle \zeta (s)}...
perform some kind of regularization. The most popular of which for computing functional determinants is the zetafunctionregularization. For instance, this...
practice both numbers are often infinite so are defined using zetafunctionregularization. It was introduced by Atiyah, Patodi, and Singer (1973, 1975)...
^{2}}{6\gamma }}\end{aligned}}} also hold true. The digamma function appears in the regularization of divergent integrals ∫ 0 ∞ d x x + a , {\displaystyle...
In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function defined as: erf z = 2 π ∫ 0 z e − t 2...
mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by...
Renormalization group UV fixed point Causal perturbation theory Zetafunctionregularization J.D. Bjorken, S. Drell (1965). Relativistic Quantum Fields, Preface...
reference. Quantum triviality Scale invariance Schröder's equation Regularization (physics) Density matrix renormalization group Functional renormalization...
first case, the multiplication is determined with some regularization of generalized function. In the second case, the algebra is constructed as multiplication...
_{N}^{\infty }{\frac {S_{f}(y)}{y^{s+1}}}dy.} General Dirichlet series Zetafunctionregularization Euler product Dirichlet convolution The formulas for both series...
equivalent to empirical risk minimization with Tikhonov regularization, where in this case the loss function is the hinge loss ℓ ( y , z ) = max ( 0 , 1 − y z...
diagram calculations into the counterterms. When using dimensional regularization, i.e. d 4 p → μ 4 − d d d p {\displaystyle d^{4}p\to \mu ^{4-d}d^{d}p}...
where the left-hand side of the equation is the two-point correlation function of the Dirac field. In a new theory, the Dirac field can interact with...
field theory String cosmology Supergravity The Elegant Universe Zetafunctionregularization Sen, Ashoke (1999-12-29). "Universality of the tachyon potential"...