## Professor Stefan Hollands

### Overview

Telephone: +44(0)29 208 70616

Fax: +44(0)29 208 74199

Extension: 70616

Location: M/2.31

#### Research Interests

Mathematical aspects of quantum field theory and (super) gravity theories.

#### Research Group

Mathematical Physics (Operator Algebras and Noncommutative Geometry)

#### Recent Significant Publications

**S. Hollands** and R. M. Wald, "Axiomatic quantum field theory in curved
spacetime," Commun. Math. Phys. 293 (2010) 85 [arXiv:0803.2003 [gr-qc]].

**S. Hollands** and H. Olbermann, "Perturbative Quantum Field Theory via Vertex
Algebras," 55pp J. Math. Phys. 50 (2009) 112304 [arXiv:0906.5313 [math-ph]].

**S. Hollands** and A. Ishibashi, "On the 'Stationary Implies Axisymmetric'
Theorem for Extremal Black Holes in Higher Dimensions," Commun. Math.
Phys. 291 (2009) 403 [arXiv:0809.2659 [gr-qc]].

**S. Hollands** and R. M. Wald, "Quantum field theory in curved spacetime, the
operator product expansion, and dark energy," Gen. Rel. Grav. 40 (2008) 2051
[Int. J. Mod. Phys. D 17 (2009) 2607] [arXiv:0805.3419 [gr-qc]].

**S. Hollands**, "Quantum field theory in terms of consistency conditions I: General
framework, and perturbation theory via Hochschild cohomology," 45pp ar-
Xiv:0802.2198 [hep-th]. Published in Sigma 5 (2009), special issue on deformation
quantization, eds. Cattaneo, Dito, Kontsevich, Sternheimer.

#### Teaching

#### Administrative Duties

Manager of 3rd Year Student Project Programme

Erasmus Coordinator

Member of School Management Board

Member of Research Committee

### Publications

**S. Hollands** and R. M. Wald, "Axiomatic quantum field theory in curved
spacetime," Commun. Math. Phys. 293 (2010) 85 [arXiv:0803.2003 [gr-qc]].

**S. Hollands** and H. Olbermann, "Perturbative Quantum Field Theory via Vertex
Algebras," 55pp J. Math. Phys. 50 (2009) 112304 [arXiv:0906.5313 [math-ph]].

**S. Hollands** and A. Ishibashi, "On the 'Stationary Implies Axisymmetric'
Theorem for Extremal Black Holes in Higher Dimensions," Commun. Math.
Phys. 291 (2009) 403 [arXiv:0809.2659 [gr-qc]].

**S. Hollands** and R. M. Wald, "Quantum field theory in curved spacetime, the
operator product expansion, and dark energy," Gen. Rel. Grav. 40 (2008) 2051
[Int. J. Mod. Phys. D 17 (2009) 2607] [arXiv:0805.3419 [gr-qc]].

**S. Hollands**, "Quantum field theory in terms of consistency conditions I: General
framework, and perturbation theory via Hochschild cohomology," 45pp ar-
Xiv:0802.2198 [hep-th]. Published in Sigma 5 (2009), special issue on deformation
quantization, eds. Cattaneo, Dito, Kontsevich, Sternheimer.

**S. Hollands** and S. Yazadjiev, "A Uniqueness theorem for 5-dimensional Einstein-
Maxwell black holes," arXiv:0711.1722 [gr-qc] Class. Quant. Grav. 25 (2008)
095010.

A. J. Amsel, T. Hertog, **S. Hollands** and D. Marolf, "A tale of two superpotentials:
Stability and instability in designer gravity," arXiv:hep-th/0701038, Phys. Rev.
D75, 084008, 2007, Erratum-ibid. D77 049903, 2008.

**S. Hollands** and D. Marolf, "Asymptotic generators of fermionic charges and
boundary conditions preserving supersymmetry," arXiv:gr-qc/0611044, Class.
Quant. Grav. 24, 2301-2332, 2007.

**S. Hollands**, A. Ishibashi and R. M. Wald, "A Higher Dimensional Stationary
Rotating Black Hole Must Be Axisymmetric," arXiv:gr-qc/0605106, Commun.
Math. Phys. 271, 699-722, 2007.

**S. Hollands**, "The Operator Product Expansion For Perturbative Quantum Field
Theory In Curved Spacetime," arXiv:gr-qc/0605072, Commun. Math. Phys. 273,
1-36, 2007.

C. D'Antoni and **S. Hollands**, "Nuclearity, local quasiequivalence and split
property for Dirac quantum fields in curved spacetime," arXiv:math-ph/0106028,
Commun. Math. Phys. 261, 133-159 (2006).

T. Hertog and **S. Hollands**, "Stability in designer gravity," arXiv:hep-th/0508181,
Class. Quant. Grav. 22 (2005) 5323-5342.

**S. Hollands**, "Quantum field theory in curved spacetime," 19pp, Prepare
for Workshop on Renormalization and Universality in Mathematical Physics,
Toronto, Canada, 18-22 Oct 2005.

**S. Hollands**, A. Ishibashi and D. Marolf, "Counter-term charges generate bulk
symmetries," arXiv:hep-th/0503105, Phys. Rev. D 72 (2005) 104025.

**S. Hollands**, A. Ishibashi and D. Marolf, "Comparison between various notions
of conserved charges in asymptotically AdS-spacetimes," arXiv:hep-th/0503045,
Class. Quant. Grav. 22, 2881-2920 (2005).

R. Brunetti, K. Fredenhagen and **S. Hollands**, "A remark on alpha vacua for
quantum field theories on de Sitter space," arXiv:hep-th/0503022, JHEP 0505,
063 (2005).

C. J. Fewster and **S. Hollands**, "Quantum energy inequalities in two-dimensional
conformal field theory," arXiv:math-ph/0412028, Rev. Math. Phys. 17, 577 (2005).

**S. Hollands** and R. M. Wald, "Conservation of the stress tensor in interacting
quantum field theory in curved spacetimes," [arXiv:gr-qc/0404074]. Rev. Math.
Phys. 17, 227-312 (2005).

**S. Hollands** and A. Ishibashi, "Asymptotic flatness and Bondi energy in higher
dimensional gravity," [arXiv:gr-qc/0304054], J. Math. Phys. 46, 022503 (2005).

**S. Hollands** and R. M. Wald, "Conformal null infinity does not exist for radiating
solutions in odd spacetime dimensions," arXiv:gr-qc/0407014, Class. Quant.
2 Grav. 21, 5139-5146 (2004).

**S. Hollands** and R. M. Wald, "Quantum field theory is not merely quantum mechanics
applied to low energy effective degrees of freedom," [arXiv:gr-qc/0405082].
Gen. Rel. Grav. 36, 2595-2603 (2004).

**S. Hollands**, "Algebraic approach to the 1/N expansion in quantum field theory,"
[arXiv:math-ph/0309042], Rev. Math. Phys. 16, 509-552 (2004).

**S. Hollands**, "A general PCT theorem for the operator product expansion in
curved spacetime," [arXiv:gr-qc/0212028], Commun. Math. Phys. 244, 209-244
(2004).

**S. Hollands** and R. M.Wald, "On the renormalization group in curved spacetime,"
[arXiv:gr-qc/0209029], Commun. Math. Phys. 237, 123-160 (2003).

**S. Hollands** and R. M. Wald, "An alternative to inflation," [arXiv:gr-qc/0205058],
Gen. Rel. Grav. 34, 2043-2055 (2002).

**S. Hollands** and R. M. Wald, "Existence of local covariant time ordered products
of quantum fields in curved spacetime," [arXiv:gr-qc/0111108], Commun. Math.
Phys. 231, 309-345 (2002).

**S. Hollands** and W. Ruan, "The state space of perturbative quantum field theory
in curved space-times," [arXiv:gr-qc/0108032], Annales Henri Poincare 3, 635-657
(2002).

**S. Hollands** and R. M. Wald, "Local Wick polynomials and time ordered products
of quantum fields in curved spacetime," [arXiv:gr-qc/0103074], Commun. Math.
Phys. 223, 289-326 (2001).

**S. Hollands**, "Noether charges corresponding to Killing vectors for self-interacting
quantum field theories in curved spacetime," [arXiv:gr-qc/0011069], Annalen
Phys. 10, 859-883 (2001).

**S. Hollands**, "The Hadamard condition for Dirac fields and adiabatic states on
Robertson-Walker spacetimes," [arXiv:gr-qc/9906076], Commun. Math. Phys.
216, 635-661 (2001).

**S. Hollands** and M. Muller-Preussker, "Definition of magnetic monopole numbers
for SU(N) lattice gauge-Higgs models," [arXiv:hep-th/9901114], Phys. Rev. D 63,
094503 (2001).

**S. Hollands** and A. Ishibashi, "Asymptotic flatness at null infinity in higher
dimensional gravity," arXiv:hep-th/0311178.

**S. Hollands** and R. M. Wald, "Comment on inflation and alternative cosmology,"
14pp, arXiv:hep-th/0210001.

**S. Hollands** and S. Yazadjiev, "Uniqueness theorem for 5-dimensional black
holes with two axial Killing fields," 21pp, arXiv:0707.2775 [gr-qc], to appear in
Commun. Math. Phys.

**S. Hollands**, "Renormalized Quantum Yang-Mills Fields in Curved Spacetime,"
140pp, arXiv:0705.3340 [gr-qc], to appear in Rev. Math. Phys.

**S. Hollands** and G. Leiler, "On the derivation of the Boltzmann equation in quantum
field theory: Flat spacetime," 53pp arXiv:1003.1621 [cond-mat.stat-mech].

**S. Hollands**, J. Holland and A. Ishibashi, "Further restrictions on the topology
of stationary black holes in five dimensions," 22pp arXiv:1002.0490 [gr-qc].
Submitted to Ann. H. Poincare.

**S. Hollands** and A. Ishibashi, "All vacuum near horizon geometries in arbitrary
dimensions," 25pp arXiv:0909.3462 [gr-qc]. To appear in Class. Quant. Grav.

**S. Hollands** and S. Yazadjiev, "A uniqueness theorem for stationary Kaluza-Klein
black holes," 38pp arXiv:0812.3036 [gr-qc]. submitted to Commun. Math. Phys.

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### Research

#### Research Interests

My main scientific interest is in the areas of general relativiy and quantum field theory, as well as especially in the interplay between the two. General relativity is the current theory of gravitation, and its main idea is that the gravitational force ought to be thought of as the "curvature of space". Quantum field theory, on the other hand, describes quantized fields (such as the electromagnetic field) and is the formalism underlying our current understanding of elementary particles. A framework in which the two theories make contact in a very concrete way is the theory of quantized fields in curved space, and this has been the center of my interest in recent years. This theory is able to describe many exciting physical effects (fluctuations in the early Universe, black hole radiance, particle creation induced by gravity...), and its formalism also has connections to many cutting edge areas of mathematics (operator algebras, geometry, microlocal analysis, combinatorics, category theory,...). My interests are shared in part by members of the operator algebra group at Cardiff.

### Postgraduate Students

#### Graduated (Since 2000)

Nils-Ole Walliser (Diploma, Germany)

Eric Morfa-Morales (Diploma, Germany)

Sebastian Jaeger (Diploma, Germany)

Gregor Leiler (PhD, Cardiff)

Heiner Olbermann (PhD, Cardiff)

#### Current

### Biography

Diploma – Technical University Berlin (Germany)

PhD – University of York (UK)

#### Curriculum Vitae

**1996 **

Diploma Thesis, Technical University Berlin (Germany)

**1997**

Humboldt University Berlin (Germany)

**1997 - 2000**

PhD, University of York (UK)

**2000 **

University of Rome II (Italy)

**2000 - 2004**

Research Associate, University of Chicago, EFI (USA)

**2004 - 2005**

Research Associate, University of California at Santa Barbara (USA)

**2005 - 2007**

Juniorprofessor, Georg-August University Göttingen (Germany)

**2007 - Present**

Reader in Mathematical Physics, Cardiff University (UK)