# Counterterm

## Definitions

• Webster's Revised Unabridged Dictionary
• n Counterterm A term or word which is the opposite of, or antithesis to, another; an antonym; -- the opposite of synonym; as, “foe” is the counterterm of “friend”.
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Century Dictionary and Cyclopedia
• n counterterm A term opposed or contrary to another term; an antithetical term.
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## Usage

### In science:

Then the potential ΦR is R on it, and the counterterms equal 0.
Gibbs and Quantum Discrete Spaces
Note that φ(j) R (Γ) are similar to counterterms of the standard renormalization theory.
Gibbs and Quantum Discrete Spaces
It could be very interesting to understand deeply connections of these counterterms with the counterterms of quantum ﬁeld theory for models with continuous spin.
Gibbs and Quantum Discrete Spaces
Because most of counterterms come from the factor eI (C ) , this factor is key important for renormalization.
Gauge Theory of Gravity
In order to eliminate the ultraviolet divergences of the theory, we need to introduce counterterms into Lagrangian.
Gauge Theory of Gravity
All these counterterms are formally denoted by δL.
Gauge Theory of Gravity
Because δL contains all counterterms, ∼ Lef f is the Lagrangian density after complete renormalization.
Gauge Theory of Gravity
For a renormalizable theory, the counterterm δL only contain ﬁnite unknown parameters which are needed to be determined by experiments.
Gauge Theory of Gravity
Quantum ﬁeld theories generically have counterterms, and the correspondence suggests that these counterterms should be geometric invariants of the induced metric on the boundary at inﬁnity.
GR16: Quantum General Relativity
The counterterm needed to remove it can not be written in terms of R d2x ϕi ⋆ ϕi ⋆ ϕj ⋆ ϕj and R d2x ϕi ⋆ ϕj ⋆ ϕi ⋆ ϕj . A possible way to remove this divergence is by generalizing the deﬁnition of 1PI diagram.
Noncommutative Supersymmetric Theories
To utilize this formalism it will then be necessary to show that the existence of this residual supersymmetry can constrain the radiative corrections suﬃciently to eliminate dangerous gauge-violating counterterms.
Lattice Supersymmetry and Topological Field Theory
Its power is not restricted to computing just the counterterms – it is well suited for deriving ﬁnite quantum corrections in the framework of the derivative expansion.
Low-energy dynamics in N = 2 super QED: Two-loop approximation
Therefore, higher dimension operators are needed as counterterms, and one is naturally led to the effective ﬁeld theories (EFT) .
Power corrections in models with extra dimensions
Even when using cutoffs one has to add counterterms from higher order operators, absorb the cutoff and express the result in terms of a series of unknown coeﬃcients.
Power corrections in models with extra dimensions
Ohta, “Surface counterterms and boundary stress-energy tensors for asymptotically non-anti-de Sitter spaces,” Phys.
General Definition of Gravitational Tension
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