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Beyond the Nanoworld: Quarks, Leptons, and Gauge Bosons
https://books.google.com/books?isbn=1439865213
H. G. Dosch - 2008 - Science
To do so I shall have to return to the essence of gauge invariance. As an analogy, I shall discuss the introduction of a new currency, the euro, in several ... like a “[PDF]The symmetry and simplicity of the laws of physics ... - arXiv
arxiv.org/pdf/1410.6753
arXiv
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by J Maldacena - 2014 - Cited by 1 - Related articles
be a solid cylinder or a hollow cylinder, but both will roll smoothly on a table. ... The analogy between foreign exchange and lattice gauge theory was noted ... is euros. Suppose that the exchange rate posted by the bank at the bridge between two ... day the local government decides that they will change their currency units.[PDF]Gauge transforms in stochastic investment modelling.
www.actuaries.org/.../Smith_Speed.pd...
International Actuarial Association
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[PS]GAUGE PHYSICS OF FINANCE 1. Informal Sketch There is ...
www.phy.bme.hu/.../...
Budapest University of Technology and Economics
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The symmetry and simplicity of the
laws of physics and the Higgs boson
Juan Maldacena
Institute for Advanced Study, Princeton, NJ 08540, USA
laws of physics and the Higgs boson
Juan Maldacena
Institute for Advanced Study, Princeton, NJ 08540, USA
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In physics, we imagine that this story about countries and exchange rates is happening
at very, very short distances, much shorter than the ones we can measure today. When we
look at any physical system, even empty space, we are looking at all these countries from
very far away, so that they look like a continuum. See gure 8. When an electron is moving
in the vacuum, it is seamlessly moving from a point in spacetime to the next. In the very
microscopic description, it would be constantly changing between the di erent countries,
changing the money it is carrying, and becoming \richer" in the process. In physics we
do not know whether there is an underlying discrete structure like the countries we have
described. However, when we do computations in gauge theories we often assume a discrete
structure like this one and then take the continuum limit when all the countries are very
at very, very short distances, much shorter than the ones we can measure today. When we
look at any physical system, even empty space, we are looking at all these countries from
very far away, so that they look like a continuum. See gure 8. When an electron is moving
in the vacuum, it is seamlessly moving from a point in spacetime to the next. In the very
microscopic description, it would be constantly changing between the di erent countries,
changing the money it is carrying, and becoming \richer" in the process. In physics we
do not know whether there is an underlying discrete structure like the countries we have
described. However, when we do computations in gauge theories we often assume a discrete
structure like this one and then take the continuum limit when all the countries are very
Electromagnetism is based on a similar gauge symmetry. In fact, at each point in
spacetime the symmetry corresponds to the symmetry of rotations of a circle. One way
to picture it is to imagine that at each point in spacetime we have an extra circle, an
extra dimension. See gure 9(a). The \country" that is located at each point in spacetime
chooses a way to de ne angles on this extra circle in an independent way. More precisely,
each \country" chooses a point on the circle that they call \zero angle" and then describe
the position of any other point in terms of the angle relative to this point. This is like
choosing the currency in the economic example. Now, in physics, we do not know whether
this circle is real. We do not know if indeed there is an extra dimension. All we know
is that the symmetry is similar to the symmetry we would have if there was an extra
dimension. In physics we like to make as few assumptions as possible. An extra dimension
is not a necessary assumption, only the symmetry is. Also the only relevant quantities
are the magnetic potentials which tell us how the position of a particle in the extra circle
changes as we go from one point in spacetime to its neighbor.
spacetime the symmetry corresponds to the symmetry of rotations of a circle. One way
to picture it is to imagine that at each point in spacetime we have an extra circle, an
extra dimension. See gure 9(a). The \country" that is located at each point in spacetime
chooses a way to de ne angles on this extra circle in an independent way. More precisely,
each \country" chooses a point on the circle that they call \zero angle" and then describe
the position of any other point in terms of the angle relative to this point. This is like
choosing the currency in the economic example. Now, in physics, we do not know whether
this circle is real. We do not know if indeed there is an extra dimension. All we know
is that the symmetry is similar to the symmetry we would have if there was an extra
dimension. In physics we like to make as few assumptions as possible. An extra dimension
is not a necessary assumption, only the symmetry is. Also the only relevant quantities
are the magnetic potentials which tell us how the position of a particle in the extra circle
changes as we go from one point in spacetime to its neighbor.
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