Number-Theory Renormalization of Vacuum Energy

, the vacuum energy (both bosonic and fermionic) is zero if the Hamiltonian is a function of the square of the momentum, and the calculation of the vacuum energy is performed in the ring of residue classes modulo

N

. This fact is related to a problem from number theory about the number of ways to represent a number as a sum of

d

squares in the ring of residue classes modulo

N

.

Note:

33 pages, 7 figures

number theory
lattice QFT
vacuum energy
renormalization
vacuum state: energy
number theory
lattice
Hamiltonian
renormalization

References(11)

Figures(7)

[1]

Renormalization : An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion

John C. Collins
(
- IIT, Chicago
)

- ,
- ,
•
DOI:
- 10.1017/9781009401807

[2]

$p$ -Adic Analysis and Mathematical Physics

V.S. Vladimirov
,
I.V. Volovich
,
E.I. Zelenov

•
DOI:
- 10.1142/1581

[3]

Number theory as the ultimate physical theory

I.V. Volovich

- Anal.Appl. 2 (2010) 77-87
•
DOI:
- 10.1134/S2070046610010061

[4]

Assumption and Myth in Physical Theory

H. Bondi

[5]

Binary representation of coordinate and momentum in quantum mechanics

M.G. Ivanov

- Theor.Math.Phys. 196 (2018) 1, 1002-1017,
- Teor.Mat.Fiz. 196 (2018) 1, 70-87
•
DOI:
- 10.1134/S0040577918070073

Ternary and binary representation of coordinate and momentum in quantum mechanics

M.G. Ivanov
(
- Moscow, MIPT
)
,
A.Yu. Polushkin
(
- Moscow, MIPT
)

- AIP Conf.Proc. 2362 (2021) 1, 040002
•
e-Print:
- 2009.13618
•
DOI:
- 10.1063/5.0055033

[7]

Digital representation of continuous observables in quantum mechanics

- Teor.Mat.Fiz. 218 (2024) 3, 464-482,
- Theor.Math.Phys. 218 (2024) 3, 464-482
•
e-Print:
- 2301.09348
•
DOI:
- 10.4213/tmf10536

[8]

Arithmetic of Quadratic Forms

V.V. Dotsenko

[9]

The computer as a new reality of mathematics. II. The Waring problem

N.A. Vavilov

[10]

Elements of Number Theory

I.M. Vinogradov

[11]

Number Theory

I.R. Shafarevich
,
Z.I. Borevich