What is qft

This step helps people think metacognitively about how they used questions to learn. It allows them to reflect on new lines of thinking they may have developed. Visit rightquestion. As long as you include this source language, you are welcome to use, adapt, and share our strategies and materials for noncommercial use. The hundreds of free resources you will find on our network will help you easily move into action to learn a strategy one day and facilitate the very next.

What is the QFT? Using the QFT with adults Groups of parents work together to generate questions. Steps of the QFT The steps of the QFT are designed to stimulate three types of thinking: divergent thinking, convergent thinking, and metacognitive thinking. Introduce the rules Introduce the four essential rules for producing questions: Ask as many questions as you can.

Do not stop to discuss, judge, or answer the questions. Write down every question exactly as it is stated. Change any statement into a question. Remind people to follow the rules each time you use the technique. Which rule might be most difficult to follow? Introduce the Question Focus and produce questions Notice how producing questions is just one relatively quick step in the QFT process. Improve questions Participants work with the questions they produced.

Prioritize questions Prioritization instructions should bring participants back to the central objective. Discuss next steps How will questions be used? Reflect Participants should reflect: What did you learn? How can you use what you learned? General tips for facilitation The role of the QFT-leader is to facilitate the participants moving through the different steps of the QFT as simply as possible.

We call this person the facilitator. In a classroom, the teacher is the one who facilitates the QFT. Monitor group work and give clarifying instructions as needed.

Go around the room to observe group work and interactions during the process. Listen for the types of questions participants are asking. Proceeding this way makes it easier to evaluate the force of the following arguments in a more balanced manner.

Since various arguments seem to speak against a particle interpretation, the allegedly only alternative, namely a field interpretation, is often taken to be the appropriate ontology of QFT.

So let us see what a physical field is and why QFT may be interpreted in this sense. Thus a field is a system with an infinite number of degrees of freedom, which may be restrained by some field equations. Whereas the intuitive notion of a field is that it is something transient and fundamentally different from matter, it can be shown that it is possible to ascribe energy and momentum to a pure field even in the absence of matter.

This somewhat surprising fact shows how gradual the distinction between fields and matter can be. Thus there is an obvious formal analogy between classical and quantum fields: in both cases field values are attached to space-time points, where these values are specified by real numbers in the case of classical fields and operators in the case of quantum fields. Due to this formal analogy it appears to be beyond any doubt that QFT is a field theory. But is a systematic association of certain mathematical terms with all points in space-time really enough to establish a field theory in a proper physical sense?

Is it not essential for a physical field theory that some kind of real physical properties are allocated to space-time points?

This requirement seems not fulfilled in QFT, however. Teller ch. Only a specific configuration , i. There are at least four proposals for a field interpretation of QFT, all of which respect the fact that the operator-valuedness of quantum fields impedes their direct reading as physical fields. The main problem with proposal i , and possibly with ii , too, is that an expectation value is the average value of a whole sequence of measurements, so that it does not qualify as the physical property of any actual single field system, no matter whether this property is a pre-existing or categorical value or a propensity or disposition.

But this is also a problem for the VEV interpretation: While it shows nicely that much more information is encoded in the quantum field operators than just unspecifically what could be measured, it still does not yield anything like an actual field configuration.

While this last requirement is likely to be too strong in a quantum theoretical context anyway, the next proposal may come at least somewhat closer to it. Correspondingly, it is the most widely discussed extant proposal; see, e. In effect, it is not very different from proposal i , and with further assumptions for i even identical. However, proposal ii phrases things differently and in a very appealing way.

The basic idea is that quantized fields should be interpreted completely analogously to quantized one-particle states, just as both result analogously from imposing canonical commutation relations on the non-operator-valued classical quantities.

Thus just as a quantum state in ordinary single-particle QM can be interpreted as a superposition of classical localized particle states, the state of a quantum field system, so says the wave functional approach, can be interpreted as a superposition of classical field configurations. In practice, however, QFT is hardly ever represented in wave functional space because usually there is little interest in measuring field configurations.

The multitude of problems for particle as well as field interpretations prompted a number of alternative ontological approaches to QFT. Auyang and Dieks propose different versions of event ontologies. In recent years, however, ontic structural realism OSR has become the most fashionable ontological framework for modern physics. While so far the vast majority of studies concentrates on ordinary QM and General Relativity Theory, it seems to be commonly believed among advocates of OSR that their case is even stronger regarding QFT, in light of the paramount significance of symmetry groups also see below —hence the name group structural realism Roberts Explicit arguments are few and far between, however.

Cao b points out that the best ontological access to QFT is gained by concentrating on structural properties rather than on any particular category of entities. The central significance of gauge theories in modern physics may support structural realism.

Lyre claims that only ExtOSR is in a position to account for gauge theories. Moreover, it can make sense of zero-value properties, such as the zero mass of photons. Category theory could be a promising framework for OSR in general and QFT in particular, because the main reservation against the radical but also seemingly incoherent idea of relations without relata may depend on the common set theoretic framework.

See SEP entries on structural realism 4. Superselection sectors are inequivalent irreducible representations of the algebra of all quasi-local observables.

Since we are dealing with quantum physical systems many properties are dispositions or propensities ; hence the name dispositional trope ontology. A trope bundle is not individuated via spatio-temporal co-localization but because of the particularity of its constitutive tropes. Morganti also advocates a trope-ontological reading of QFT, which refers directly to the classification scheme of the Standard Model. In other words the state space of an elementary system shall have no internal structure with respect to relativistic transformations.

Put more technically, the state space of an elementary system must not contain any relativistically invariant subspaces, i. If the state space of an elementary system had relativistically invariant subspaces then it would be appropriate to associate these subspaces with elementary systems.

The requirement that a state space has to be relativistically invariant means that starting from any of its states it must be possible to get to all the other states by superposition of those states which result from relativistic transformations of the state one started with.

Doing that involves finding relativistically invariant quantities that serve to classify the irreducible representations. Regarding the question whether Wigner has supplied a definition of particles, one must say that although Wigner has in fact found a highly valuable and fruitful classification of particles, his analysis does not contribute very much to the question what a particle is and whether a given theory can be interpreted in terms of particles.

What Wigner has given is rather a conditional answer. For instance, the pivotal question of the localizability of particle states, to be discussed below, is still open.

Kuhlmann a: sec. It thus appears to be impossible that our world is composed of particles when we assume that localizability is a necessary ingredient of the particle concept. So far there is no single unquestioned argument against the possibility of a particle interpretation of QFT but the problems are piling up. The Reeh-Schlieder theorem is thus exploiting long distance correlations of the vacuum.

Or one can express the result by saying that local measurements do not allow for a distinction between an N-particle state and the vacuum state. Malament formulates a no-go theorem to the effect that a relativistic quantum theory of a fixed number of particles predicts a zero probability for finding a particle in any spatial set, provided four conditions are satisfied, namely concerning translation covariance, energy, localizability and locality.

The localizability condition is the essential ingredient of the particle concept: A particle—in contrast to a field—cannot be found in two disjoint spatial sets at the same time.

It requires that the statistics for measurements in one space-time region must not depend on whether or not a measurement has been performed in a space-like related second space-time region. A relativistic quantum theory of a fixed number of particles, satisfying in particular the localizability and the locality condition, has to assume a world devoid of particles or at least a world in which particles can never be detected in order not to contradict itself.

One is forced towards QFT which, as Malament is convinced, can only be understood as a field theory. This is even the case arbitrarily close after a sharp position measurement due to the instantaneous spreading of wave packets over all space.

Note, however, that ordinary QM is non-relativistic. A conflict with SRT would thus not be very surprising although it is not yet clear whether the above-mentioned quantum mechanical phenomena can actually be exploited to allow for superluminal signalling.

The local behavior of phenomena is one of the leading principles upon which the theory was built. This makes non-localizability within the formalism of QFT a much severer problem for a particle interpretation. According to Saunders it is the localizability condition which might not be a natural and necessary requirement on second thought. One can only require for the same kind of event not to occur at both places. The question is rather whether QFT speaks about things at all.

One thing seems to be clear. Does the field interpretation also suffer from problems concerning non-localizability? This procedure leads to operator-valued distributions instead of operator-valued fields. The lack of field operators at points appears to be analogous to the lack of position operators in QFT, which troubles the particle interpretation. However, for position operators there is no remedy analogous to that for field operators: while even unsharply localized particle positions do not exist in QFT see Halvorson and Clifton , theorem 2 , the existence of smeared field operators demonstrates that there are at least point-like field operators.

Symmetries play a central role in QFT. In order to characterize a special symmetry one has to specify transformations T and features that remain unchanged during these transformations: invariants I. The basic idea is that the transformations change elements of the mathematical description the Lagrangians for instance whereas the empirical content of the theory is unchanged.

There are space-time transformations and so-called internal transformations. Whereas space-time symmetries are universal, i. The invariance of a system defines a conservation law, e. Inner transformations, such as gauge transformations, are connected with more abstract properties. Symmetries are not only defined for Lagrangians but they can also be found in empirical data and phenomenological descriptions. If a conservation law is found one has some knowledge about the system even if details of the dynamics are unknown.

The analysis of many high energy collision experiments led to the assumption of special conservation laws for abstract properties like baryon number or strangeness. Evaluating experiments in this way allowed for a classification of particles. This phenomenological classification was good enough to predict new particles which could be found in the experiments.

Free places in the classification could be filled even if the dynamics of the theory for example the Lagrangian of strong interaction was yet unknown. As the history of QFT for strong interaction shows, symmetries found in the phenomenological description often lead to valuable constraints for the construction of the dynamical equations. Arguments from group theory played a decisive role in the unification of fundamental interactions.

In addition, symmetries bring about substantial technical advantages. For example, by using gauge transformations one can bring the Lagrangian into a form which makes it easy to prove the renormalizability of the theory. See also the entry on symmetry and symmetry breaking. To a remarkable degree the present theories of elementary particle interactions can be understood by deduction from general principles. Under these principles symmetry requirements play a crucial role in order to determine the Lagrangian.

For example, the only Lorentz invariant and gauge invariant renormalizable Lagrangian for photons and electrons is precisely the original Dirac Lagrangian. In this way symmetry arguments acquire an explanatory power and help to minimize the unexplained basic assumptions of a theory. Since symmetry operations change the perspective of an observer but not the physics an analysis of the relevant symmetry group can yield very general information about those entities which are unchanged by transformations.

Such an invariance under a symmetry group is a necessary but not sufficient requirement for something to belong to the ontology of the considered physical theory. Hermann Weyl propagated the idea that objectivity is associated with invariance see, e. Auyang stresses the connection between properties of physically relevant symmetry groups and ontological questions. Symmetries are typical examples of structures that show more continuity in scientific change than assumptions about objects.

Physical objects such as electrons are then taken to be similar to fiction that should not be taken seriously, in the end. In the epistemic variant of structural realism structure is all we know about nature whereas the objects which are related by structures might exist but they are not accessible to us.

For the extreme ontic structural realist there is nothing but structures in the world Ladyman A particle interpretation of QFT answers most intuitively what happens in particle scattering experiments and why we seem to detect particle trajectories. Moreover, it would explain most naturally why particle talk appears almost unavoidable.

However, the particle interpretation in particular is troubled by numerous serious problems. Besides localizability, another hard core requirement for the particle concept that seems to be violated in QFT is countability.

First, many take the Unruh effect to indicate that the particle number is observer or context dependent. At first sight the field interpretation seems to be much better off, considering that a field is not a localized entity and that it may vary continuously—so no requirements for localizability and countability.

Accordingly, the field interpretation is often taken to be implied by the failure of the particle interpretation. However, on closer scrutiny the field interpretation itself is not above reproach. In order to get determinate physical properties, or even just probabilities, one needs a quantum state. However, since quantum states as such are not spatio-temporally defined, it is questionable whether field values calculated with their help can still be viewed as local properties.

The second serious challenge is that the arguably strongest field interpretation—the wave functional version—may be hit by similar problems as the particle interpretation, since wave functional space is unitarily equivalent to Fock space.

The occurrence of unitarily inequivalent representations UIRs , which first seemed to cause problems specifically for the particle interpretation but which appears to carry over to the field interpretation, may well be a severe obstacle for any ontological interpretation of QFT.

The two remaining contestants approach QFT in a way that breaks more radically with traditional ontologies than any of the proposed particle and field interpretations.

Ontic Structural Realism OSR takes the paramount significance of symmetry groups to indicate that symmetry structures as such have an ontological primacy over objects. However, since most OSRists are decidedly against Platonism, it is not altogether clear how symmetry structures could be ontologically prior to objects if they only exist in concrete realizations, namely in those objects that exhibit these symmetries.

In conclusion one has to recall that one reason why the ontological interpretation of QFT is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place.

And it looks as if that problem will persist for quite some time. What is QFT? The Basic Structure of the Conventional Formulation 2. Beyond the Standard Model 3. Further Philosophical Issues 5. Figure 1. Bibliography Arageorgis, A.

Auyang, S. Bain, J. Baker, D. Born, M. Heisenberg, and P. Brading, K. Castellani eds. Bratteli, O. Buchholz, D. Sen and A. Gersten, eds. Breitenlohner and D. Maison, eds, Quantum Field Theory. Proceedings of the Ringberg Workshop , pp. Busch, P. Butterfield, J.

Halvorson eds. Pagonis eds. Callender, C. Huggett eds. Cao, T. Castellani, E. Clifton, R. Davies, P. Dawid, R. Dieks, D. Dirac, P. Earman, J. Egg, M. Eva, B. Feintzeig, B. Fell, J. Fleming, G. Fraser, D. Fraser, J. Greene, B. Norton and Company.

Haag, R. Halvorson, H. Hartmann, S. Healey, R. Heisenberg, W. Hoddeson, L. Brown, M. Riordan, and M. Dresden eds. Horuzhy, S. Huggett, N. Clark and K. Hawley, eds. Johansson, L. Kadison, R. Kaku, M. Kantorovich, A. Kastler, D. Kiefer, C. Second edition. Kronz, F. The crowning glory of the standard model came in , with the discovery of the Higgs boson , predicted almost five decades earlier.

Mass is the most solid property of matter, and the mass of a fundamental particle is determined by its degree of interaction with the Higgs boson. According to a theory first proposed in , the molasses-like field associated with the Higgs provides a drag that varies according to particle type.

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