On the phi(4) field theoretical model for the action potential. Maska, M. & Pietruszka, M. Journal of Biological Physics, 21(3):211-222, 1995.
abstract   bibtex   
In this short letter we report on the possibility of a field-theoretical\nmodel of the action potential in biological membranes. In order to\ngive a qualitative description of the (K+ and N alpha(+) driven)\nprocess of propagation of the action potential we introduce two classical\nscalar fields phi and psi representing N alpha(+) and K+ ions, respectively.\nThese fields are described by the Lagrangian densities L(phi) and\nL(psi). Moreover, we add the interaction term L((phi psi)) between\nthe fields. The Lagrangian densities L(phi) and L(psi), include a\ndouble-well potential that leads to a spontaneous symmetry breaking\n(SSB) which may produce topologically non-trivial structures (i.e.\nstructures with non-zero topological charge). In order to describe\nthe transversal motion of K+ and N alpha(+) ions we have to assume\nnonuniform solutions. Eventually, after deriving the Euler-Lagrange\nsystem of equations of motion we perform the Lorentz transformation\n(boost) on the static solution.
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 title = {On the phi(4) field theoretical model for the action potential},
 type = {article},
 year = {1995},
 keywords = {action potential nerve conduction spontaneous symm},
 created = {2014-12-04T23:36:42.000Z},
 pages = {211-222},
 volume = {21},
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 abstract = {In this short letter we report on the possibility of a field-theoretical\nmodel of the action potential in biological membranes. In order to\ngive a qualitative description of the (K+ and N alpha(+) driven)\nprocess of propagation of the action potential we introduce two classical\nscalar fields phi and psi representing N alpha(+) and K+ ions, respectively.\nThese fields are described by the Lagrangian densities L(phi) and\nL(psi). Moreover, we add the interaction term L((phi psi)) between\nthe fields. The Lagrangian densities L(phi) and L(psi), include a\ndouble-well potential that leads to a spontaneous symmetry breaking\n(SSB) which may produce topologically non-trivial structures (i.e.\nstructures with non-zero topological charge). In order to describe\nthe transversal motion of K+ and N alpha(+) ions we have to assume\nnonuniform solutions. Eventually, after deriving the Euler-Lagrange\nsystem of equations of motion we perform the Lorentz transformation\n(boost) on the static solution.},
 bibtype = {article},
 author = {Maska, M and Pietruszka, M},
 journal = {Journal of Biological Physics},
 number = {3}
}

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