国家自然科学基金委创新群体报告

Irreducible Loop Integrals (ILIs)
Loop Regularization (LORE)

Yue-Liang Wu, SYMMETRY PRESERVING LOOP
REGULARIZATION AND RENORMALIZATION OF QFTS. Mod.Phys.Lett.A19:2004, 2191-2204.
Why Quantum Field Theory So Successful
Lorentz and CPT Violation in QFT

QFT may not be an underlying theory but EFT In String Theory, Lorentz invariance can be broken down spontaneously. Lorentz non-invariant quantum field theory Explicit、Spontaneous 、Induced CPT/Lorentz violating Chern-Simons term constant vector

All the regularizations have their advantages and shortcomings
Criteria of Consistent Regularization
(i) The regularization is rigorous that it can maintain the basic symmetry principles in the original theory, such as: gauge invariance, Lorentz invariance and translational invariance (ii) The regularization is general that it can be applied to both underlying renormalizable QFTs (such as QCD) and effective QFTs (like the gauged Nambu-JonaLasinio model and chiral perturbation theory).
for for


Regularization Scheme
Regularization scheme dependence

Ambiguity of Dimensional regularization with problem Ambiguity with momentum translation for linear divergent term Ambiguity of reducing triangle diagrams

Implication: Existence of sliding energy scale (SES) μ_s which is not related to masses of particles.

The physical effects above the SES μ_s are integrated in the renormalized couplings and fields.

Folk’s theorem by Weinberg:
Any quantum theory that at sufficiently low energy and large distances looks Lorentz invariant and satisfies the cluster decomposition principle will also at sufficiently low energy look like a quantum field theory.
Consistent Result


Statement in Literature: constant vector K can only be determined by experiment Our Conclusion: constant vector K can consistently be fixed from theoretical calculations
Diverse Results

Gauge invariance of axial-current
S.Coleman and S.L.Glashow, Phys.Rev.D59: 116008 (1999)

Pauli-Villas regularization with
D.Colladay and V.A.Kostelecky, Phys. Rev. D58:116002 (1998).
CPT and Lorentz Invariance and Violation in QFT
Yue-Liang Wu
Kavli Institute for Theoretical Physics China
Key Laboratory of Frontiers in Theoretical Physics
Diverse Results

Based on nonperturbative formulation with
R.Jackiw and V.A.Kostelecky, Phys.Rev.Lett. 82: 3572 (1999).

Derivative Expansion with dimensional regularization



Induced CTP/Lorentz Violation


Real world has been found to be successfully described by quantum field theories EQED with constant vector
mass

What is the relation ?
Symmetry-Preserving Loop Regularization (LORE) wቤተ መጻሕፍቲ ባይዱth String Mode Regulators
Yue-Liang Wu, SYMMETRY PRINCIPLE PRESERVING AND

INFINITY FREE REGULARIZATION AND RENORMALIZATION OF QUANTUM FIELD THEORIES AND THE MASS GAP. Int.J.Mod.Phys.A18:2003, 5363-5420.


How to reach a consistent regularization scheme ?
Regularization Methods

Cut-off regularization Keeping divergent behavior, spoiling gauge symmetry & translational/rotational symmetries

Renormalization group by Wilson or Gell-Mann & Low Allow to deal with physical phenomena at any interesting energy scale by integrating out the physics at higher energy scales. To be able to define the renormalized theory at any interesting renormalization scale .

Gauge invariance and conservation of vector Ward identity
M.Perez-Victoria, JHEP 0104 032 (2001).

Consistent analysis via dimensional regularization
G.Bonneau, Nucl. Phys. B593 398 (2001).


All known basic forces of nature: electromagnetic, weak, strong & gravitational forces, are governed by the local gauge symmetries: U(1)_Y x SU(2)_L x SU(3)_c x SO(1,3)
J.M.Chung and P.Oh, Phys.Rev.D60: 067702 (1999).

Keep full
dependence with
M.Perez-Victoria, Phys.Rev.Lett.83: 2518 (1999).

Keep full
dependence with
M.Perez-Victoria, Phys.Rev.Lett.83: 2518 (1999).

Indication: existence in any case a characterizing energy scale (CES) M_c At sufficiently low energy then means: E << M_c QFTs

Why Quantum Field Theory So Successful
Criteria of Consistent Regularization
(iii) The regularization is also essential in the sense that it can lead to the well-defined Feynman diagrams with maintaining the initial divergent behavior of integrals. so that the regularized theory only needs to make an infinity-free renormalization. (iv) The regularization must be simple that it can provide the practical calculations.