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Relationship between string theory and quantum field theory

Relationship between string theory and quantum field theory is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Relationship between string theory and quantum field theory rather than just read about it. In short: Many first principles in quantum field theory are explained, or get further insight, in string theory. From quantum field theory to string theory Emission and absorption: one of the most basic building blocks of quantum field theory, is the notion that particles (such as electrons) can emit and absorb other particles (such as photons).

Key takeaways

  • Relationship between string theory and quantum field theory belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Relationship between string theory and quantum field theory to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Relationship between string theory and quantum field theory from memory before moving on to harder problems.

Reference excerpt

Many first principles in quantum field theory are explained, or get further insight, in string theory.

From quantum field theory to string theory Emission and absorption: one of the most basic building blocks of quantum field theory, is the notion that particles (such as electrons) can emit and absorb other particles (such as photons). Thus, an electron may just "split" into an electron plus a photon, with a certain probability (which is roughly the coupling constant). This is described in string theory as one string splitting into two. This process is an integral part of the theory. The mode on the original string also "splits" between its two parts, resulting in two strings which possibly have different modes, representing two different particles. Coupling constant: in quantum field theory this is, roughly, the probability for one particle to emit or absorb another particle, the latter typically being a gauge boson (a particle carrying a force). In string theory, the coupling constant is no longer a constant, but is rather determined by the abundance of strings in a particular mode, the dilaton. Strings in this mode couple to the worldsheet curvature of other strings, so their abundance through space-time determines the measure by which an average string worldsheet will be curved. This determines its probability to split or connect to other strings: the more a worldsheet is curved, the higher a chance of splitting and reconnecting it has. Spin: each particle in quantum field theory has a particular spin s, which is an internal angular momentum. Classically, the particle rotates in a fixed frequency, but this cannot be understood if particles are point-like. In string theory, spin is understood by the rotation of the string; For example, a photon with well-defined spin components (i.e. in circular polarization) looks like a tiny straight line revolving around its center. Gauge symmetry: in quantum field theory, the mathematical description of physical fields include non-physical states. In order to omit these states from the description of every physical process, a mechanism called gauge symmetry is used. This is true for string theory as well, but in string theory it is often more intuitive to understand why the non-physical states should be disposed of. The simplest example is the photon: a photon is a vector particle (it has an inner "arrow" which points to some direction, its polarization). Mathematically, it can point towards any direction in space-time. Suppose the photon is moving in the z direction; then it may either point towards the x, y or z spatial directions, or towards the t (time) direction (or any diagonal direction). Physically, however, the photon may not point towards the z or t directions (longitudinal polarization), but only in the x-y plane (transverse polarization). A gauge symmetry is used to dispose of the non-physical states. In string theory, a photon is described by a tiny oscillating line, with the axis of the line being the direction of the polarization (i.e. the inner direction of the photon is the axis of the string which the photon is made of). If we look at the worldsheet, the photon will look like a long strip which stretches along the time direction with an angle towards the z-direction (because it is moving along the z-direction as time goes by); its short dimension is therefore in the x-y plane. The short dimension of this strip is precisely the direction of the photon (its polarization) in a certain moment in time. Thus the photon cannot point towards the z or t directions, and its polarization must be transverse. Note: formally, gauge symmetries in string theory are (at least in most cases) a result of the existence of a global symmetry together with the profound gauge symmetry of string theory, which is the symmetry of the worldsheet under a local change of coordinates and scales. Renormalization: in particle physics the behaviour of particles in the smallest scales is largely unknown. In order to avoid this difficulty, the particles are treated as fields behaving according to an "effective field theory" at low energy scales, and a mathematical tool known as renormalization is used to describe the unknown aspects of this effective theory using only a few parameters. These parameters can be adjusted so that calculations give adequate results. In string theory, this is unnecessary since the behaviour of the strings is presumed to be known to every scale. Fermions: in the bosonic string, a string can be described as an elastic one-dimensional object (i.e. a line) "living" in spacetime. In superstring theory, every point of the string is not only located at some point in spacetime, but it may also have a small arrow "drawn" on it, pointing at some direction in spacetime. These arrows are described by a field "living" on the string. This is a fermionic field, because at each point of the string there is only one arrow; thus one cannot bring two arrows to the same point. This fermionic field (which is a field on the worldsheet) is ultimately responsible for the appearance of fermions in spacetime: roughly, two strings with arrows drawn on them cannot coexist at the same point in spacetime, because then one would effectively have one string with two sets of arrows at the same point, which is not allowed, as explained above. Therefore two such strings are fermions in spacetime.

Notes

Worked examples

Example 1 — a first encounter with Relationship between string theory and quantum field theory

Start with the simplest possible case. Write down what Relationship between string theory and quantum field theory claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Relationship between string theory and quantum field theory before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Relationship between string theory and quantum field theory ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Relationship between string theory and quantum field theory

In research
Relationship between string theory and quantum field theory appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Relationship between string theory and quantum field theory in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Relationship between string theory and quantum field theory is common in secondary-school and first-year university syllabi. It links to neighbouring topics Quantum field theory, String theory, so understanding it makes those chapters shorter.
In everyday life
Look for Relationship between string theory and quantum field theory outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Relationship between string theory and quantum field theory in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Relationship between string theory and quantum field theory means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Relationship between string theory and quantum field theory out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Relationship between string theory and quantum field theory in simple terms?

Many first principles in quantum field theory are explained, or get further insight, in string theory. From quantum field theory to string theory Emission and absorption: one of the most basic building blocks of quantum field theory, is the notion that particles (such as electrons) can emit and abs…

Why does Relationship between string theory and quantum field theory matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Relationship between string theory and quantum field theory?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Relationship between string theory and quantum field theory.

Tags

  • Quantum field theory
  • String theory

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