# Running of Newton's constant and noninteger powers of the d'Alembertian

## Abstract

The running of Newton's constant can be taken into account by considering covariant, nonlocal generalizations of the field equations of general relativity. These generalizations involve nonanalytic functions of the d'Alembertian, as (-square lg){sup -{alpha}}, with {alpha} a noninteger number, and ln[-square lg]. In this paper we define these nonlocal operators in terms of the usual two point function of a massive field. We analyze some of their properties, and present specific calculations in flat and Robertson Walker spacetimes.

- Authors:

- Departamento de Fisica Juan Jose Giambiagi, Facultad de Ciencias Exactas y Naturales, UBA, Ciudad Universitaria, Pabellon I, 1428 Buenos Aires (Argentina)

- Publication Date:

- OSTI Identifier:
- 20935222

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.024003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONFIGURATION; COSMOLOGY; FIELD EQUATIONS; FUNCTIONS; GENERAL RELATIVITY THEORY; QUANTUM GRAVITY; SPACE-TIME

### Citation Formats

```
Lopez Nacir, D., and Mazzitelli, F. D.
```*Running of Newton's constant and noninteger powers of the d'Alembertian*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.024003.

```
Lopez Nacir, D., & Mazzitelli, F. D.
```*Running of Newton's constant and noninteger powers of the d'Alembertian*. United States. doi:10.1103/PHYSREVD.75.024003.

```
Lopez Nacir, D., and Mazzitelli, F. D. Mon .
"Running of Newton's constant and noninteger powers of the d'Alembertian". United States.
doi:10.1103/PHYSREVD.75.024003.
```

```
@article{osti_20935222,
```

title = {Running of Newton's constant and noninteger powers of the d'Alembertian},

author = {Lopez Nacir, D. and Mazzitelli, F. D.},

abstractNote = {The running of Newton's constant can be taken into account by considering covariant, nonlocal generalizations of the field equations of general relativity. These generalizations involve nonanalytic functions of the d'Alembertian, as (-square lg){sup -{alpha}}, with {alpha} a noninteger number, and ln[-square lg]. In this paper we define these nonlocal operators in terms of the usual two point function of a massive field. We analyze some of their properties, and present specific calculations in flat and Robertson Walker spacetimes.},

doi = {10.1103/PHYSREVD.75.024003},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}

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