**How Do Field Theories Refer to Entities in Fields?**

Sunny Auyang

There are two dominant theories of reference: the direct theory presupposes that the referents have
numerical identities, the descriptive theory does not. By arguing that field theories use direct reference, I explain the meaning of individual entities in the world of physical fields.

**Ontological Relativity and Fundamentality: Is QFT the Fundamental Theory?**

Tian Yu Cao

The concept of fundamentality will be defined and various senses in which whether or not QFT should be regarded as the fundamental theory will be discussed both in terms of ontology and in terms of defining features of a conceptual framework

**Local Operations and Events in Quantum Field Theory. **

Dennis Dieks

A basic concept in algebraic relativistic quantum field theory (AQFT) is the notion of a "local operation": the operators in the algebras attached to open space-time regions represent measurements performed within these regions. On the other hand, the notion of a localized physical system, or an event taking place in a restricted space-time region (ideally, an event taking place at a space-time point), does not fit in very easily with the structure of AQFT. This creates an internal tension in the theory: how are the (localized) measurement devices to be represented that perform the local operations? And don't the results of those measurements constitute localized events? In the talk we will discuss this tension and possibilities to accommodate the notion of localized event within the theory.

**Measurement and Ontology: What Kind of Evidence can we have for Quantum Fields?**

Brigitte Falkenburg

To ask for the ontology of quantum fields in terms of measurement, results in two paradoxes. (i) Ontology is about independent entities, but measurements rely on interaction. (ii) Most experimental evidences for quantum fields are based on particle tracks. My talk will explain these paradoxes in a "transcendental" approach, focusing on Wigner’s particle definition and its relation to scattering experiments; QED high precision measurements (Lamb shift,(g-2),/2); and the measurement of quark and gluon distributions in high energy scattering experiments.

**Renormalisation and the Disunities of Science**

Nick Huggett

I will discuss and reject the possibility that renormalisation means that QFT vindicates the kind of anti-foundationalist ontology sketched by Nancy Cartwright in her recent `Fundamentalism vs the Patchwork of Laws'(Proceedings of the Aristotelian Society, 1994). To do so I will develop some of the ideas of the renormalisation group, and discuss recent advances in the understanding of nonperturbative renormalisation.

**The Interpretation of Gauge Symmetry**

Micheal Redhead

The paper will pose the dilemma: Passive interpretations are mysterious in that they operate in the realm of "surplus structure" (this is reinforced by consideration of BRST symmetry), while active interpretations lead to indeterminism. The philosophical options are spelled out with as much clarity as possible.

**Three Problems about Nothing**

Simon Saunders

The paper will be about three problems of ontology in the vacuum: the Reeh-Schlieder theorem, zero-point fluctuations (and the cosmological constant problem), and Rindler quanta (and the equivalence principle).

**Bespoke or Off the Peg? Looking for an Ontology for QFT**

Peter Simons

Ontology is traditionally an a priori discipline purveying its categories and principles independently of mere facts, but this arrogance ofphilosophers has led them into latent or patent incompatibility with good science and has landed them with philosophical aporiai such as the mind-body problem and the universals dispute. So while maintaining the abstractness and systematic universality of ontology it pays to craft one's categories with an eye to the best empirical science, while not necessarily trying to read the ontology off that science. I present desiderata for a systematic ontology and give several reasons why one cannot use physical theory alone as the source of one's a posteriori ontology.

With this in mind I survey six ontological theories as possible frameworks for QFT, four briefly, two at greater length. The first is the traditional substance-attribute metaphysic, which is clearly obsolete, and on which I expend little time. The second is its modern logico-linguistic replacement, the ontology of individuals and sets touted as semantic values in logical semantics. This too falls by the wayside for several reasons. A third is the closely related ontology or ontologies of facts, against which I argue on general grounds. A fourth is Whiteheadian process ontology, which is an improvement over the previous three but still leaves several questions unsatisfactorily answered. The most flexible and promising to date is the ontology of tropes and trope bundles, which I have discussed in several places. After expounding this I reject it not because it is false but because it neither broad nor deep enough. As a final, sixth alternative, I present an ontology of invariant factors inspired in part by Whitehead and in part by remarks of Max Planck, and offer it as a promising future abstract framework within which to situate the physics of QFT.

**The Gauge argument and some questions about the QED Coupling constant**

Paul Teller

I will give an informal exposition of how to construe the so called "gauge argument" in terms of connections. In geometry we require a "connection", which functions as a rule of parallel transport, a rule which specifies which vectors at neighboring points count as "having the same direction". Specifying the derivative of a vector field must appeal to such a rule, since the derivative compares vectors at neighboring points. Similarly, when we have a complex field defined on space or space-time a derivative compares phases at neighboring points, and likewise requires appeal to a rule of "parallel phase transport". In both cases, the rule may correspond to a "flat" or a "non-flat" connection, and in the later case the non-flat case appear to correspond to a non-null electromagnetic field.

Since all that matters in appealing to a complex function in quantum theories is the comparison of phases as neighboring points, we may make an arbitrary local phase transformation, analogous to an arbitrary transformation of curvilinear coordinates in the space-time case. Continuing the analogy to the space-time case, we can think of such a local phase transformation as a transformation in the "phase coordinates". Of course when we make such a transformation we must make a correlative change in the connection if the theoretical description is to be invariant, and this comes out exactly as the familiar gauge transformation freedom of the electromagnetic field. As a result, we can see the requirement of invariance of the overall theory under a local phase transformation, construed as an arbitrary change in local "phase coordinates" as playing an epistemic role, calling our attention to the presence of a connection in the formalism, a connection which , at this level of description, may be flat or may be curved, corresponding to an electromagnetic field

However, this attractive picture is compromised when we examine the role of the QED coupling constant in this description. The connection is not the electromagnetic field, but the coupling constant times the electromagnetic field. Consequently, we cannot understand neutral particles if the gauge argument is applied to quantum mechanical wave functions - and indeed, on reflection a local phase transformation of a wave function representation of a quantum state is compensated by the correlative transformation in the operator representation, without ever needing to introduce the electromagnetic field as a compensating field. Consequently, the gauge argument can only apply to the function which is second quantized. And now the earlier conclusion, that nothing in the formalism determines whether the connection is flat or not is compromised. In the fully quantized theory, for the description to be invariant under an arbitrary change of the local phase coordinates, there must be an infraction term, so that in the presence of matter, the electromagnetic field cannot be null.

**So what IS the Quantum Field?** (Summary of the session 17:30-19:00, Monday)

P.Teller/ G. Fleming/ A. Wayne

In his An Interpretive Introduction to Quantum Field Theory Teller urged that a specific field configuration is the assignment of specific values to individual space-time points. And consequently, he claimed, the quantum field should not be construed in terms of operators assigned to space-time points, as if the operators so assigned were somehow the values of a physical quantity. Operators are like determinables. Instead, the quantum field configuration should be taken to be the expectation values associated with a specific state.

Fleming and Wayne take issue with these claims: An operator is an association of eigenvalues to eigenvectors, different such associations at each space-time point. As such, a network of dispositions is associated with each space-time point. How is this different, except in complexity, from assigning a value of the electric field to each space-time point? On the other hand, the space-time indexed expectation values associated with a specific state of the system drastically under-describe the state. Finally, the quantum operator valued field can be presented in terms of the n-point function vacuum expectation values. This presents more accurately both the similarities and differences between the operator valued quantum field and prior classical field conceptions.

Teller will agree with all these complaints but argue that an important contrast with prior field conceptions is still not coming out clearly. He will urge that there is no straightforward, simply stable "field conception" - instead there is a network of overlapping considerations, of which the book had emphasized some and the criticism are emphasizing others. More specifically, there is a range of what dispositions can be attributed to space-time points in terms of how abstract or general the dispositions are. Euler's velocity field of a material fluid is at one extreme, and the operator valued quantum field is at the other. Teller will do some work towards making out what this contrast is and how it relates to prior conceptions of the field concept. The issues go back to the origins of the field concept in reaction to worries about Newtonian action at a distance and involve a contrast between a "minimalist" field conception which does little more than summarize the equations of motion, and a more "active agent" field concept, on which we think of what is located at each point as an active agent. Many would urge that the quantum operator valued field fully qualifies as an active agent kind of field. Teller doesn't think that is clearly right. But by dinnertime it will be clear that it is also not clearly wrong.

**Teilnehmende**

Sergio Albeverio (Bonn),
Sunny Auyang (Cambridge, MA),
Jeff Barret (Irvine, CA),
Thomas Breuer (Salzburg),
Jeremy Butterfield (Cambridge, UK),
Tian Yu Cao (Boston, MA),
Martin Carrier (Bielefeld),
Elena Castellani (Florenz),
Dennis Dieks (Utrecht),
Michael Esfeld (Konstanz),
Tim Oliver Eynck (Amsterdam),
Gordon N. Fleming (University Park, PA),
Klaus Fredenhagen (Hamburg),
Cord Friebe (Freiburg i. Br.),
Thomas Görnitz (Frankfurt am Main),
Siegfried Gotzes (Wuppertal),
Frank Hättich (Paderborn),
Stephan Hartmann (Konstanz),
Carsten Held (Freiburg i. Br.),
Peter Henseler (Dortmund),
Nick Huggett (Chicago, IL),
Meinard Kuhlmann (Bremen),
Holger Lyre (Bochum),
Karl H. Menke (Bonn),
Hildegard Meyer-Ortmanns (Wuppertal),
Peter Mittelstaedt (Köln),
Gernot Münster (Münster),
Tomasz Placek (Krakau),
Gesche Pospiech (Frankfurt am Main),
Miklos Redei (Budapest),
Michael Redhead (London),
Jay F. Rosenberg (Bielefeld),
Svend E. Rugh (Denmark),
Simon Saunders (Oxford),
Elmar G. Sauter (Karlsdorf),
Joachim Schröter (Altenbeken),
Thomas Schwarzweller (Dortmund),
Johanna Seibt (Aarhus),
Peter Simons (Leeds),
Francisco José Soler Gil (Bremen),
Michael Stöltzner (Salzburg),
Christian Suhm (Münster),
Paul Teller (Davis, CA),
Eckhard Tielke (Syke),
Markus Tielke (Dortmund),
Jos Uffink (Utrecht),
Andrew Wayne (Montreal),
Henrik Zinkernagel (Kopenhagen)